: Extract the t-statistic and p-value from running `cor.test` and compare them with the t-statistic and p-value for the \"parent.sleep\" variable above by running `lm`. They should be identical. Why do you think that is?\""
]
},
{
"cell_type": "markdown",
"id": "00cf59bf",
"metadata": {},
"source": [
"# Multiple Linear Regression\n",
"\n",
"The previous linear regression model assumed a single independent variable, \"parent.sleep\", which is the number of hours slept by the parent. But what if there are other variables that could also contribute to the grumpiness of the parent? We can attempt to assess this by using a multiple linear regression, which is simply a linear regression with more than one independent variable.\n",
"\n",
"Let's add \"baby.sleep\", which is the number of hours slept by the baby, to the previous regression model. This can be easily accomplished by adding the aforementioned variable to the right side of the formula object in `lm`: "
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "334bb13b",
"metadata": {},
"outputs": [],
"source": [
"reg.model.2<-lm(formula = parent.grump ~ parent.sleep + baby.sleep, data=tutorial.dat)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "75c9c273",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Call:\n",
"lm(formula = parent.grump ~ parent.sleep + baby.sleep, data = tutorial.dat)\n",
"\n",
"Coefficients:\n",
" (Intercept) parent.sleep baby.sleep \n",
" 125.96557 -8.95025 0.01052 \n",
"\n"
]
}
],
"source": [
"print( reg.model.2 )"
]
},
{
"cell_type": "markdown",
"id": "02296af3",
"metadata": {},
"source": [
"As we can see, the coefficient associated with the number of hours slept by the parent is still large. However, the coefficient for \"baby.sleep\" is very small, suggesting that the amount of sleep the baby gets does not really matter. What really contributes to the parent's grumpiness is the amount of sleep the parent gets."
]
},
{
"cell_type": "markdown",
"id": "66c42cb8",
"metadata": {},
"source": [
"
Practice question: Create a new variable in the data frame of this tutorial, defined as the values of \"baby.sleep\" divided by 1000. Name this variable \"baby.sleep.2\", for example. Now rerun the multiple regression model again but replacing \"baby.sleep\" with \"baby.sleep.2\". \n",
" \n",
"- The associated $\\beta$ coefficient for this new variable should be larger that the one associated with \"baby.sleep\". Does that mean that \"baby.sleep.2\" is more important to the parent's grumpiness than \"baby.sleep\"? \n",
"- Similarly, now this $\\beta$ is greater than the $\\beta$ of \"parent.sleep\". Does that mean that in this case the number of hours slept by the parent is less important?\n",
"- What is wrong here?"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "64040c8a",
"metadata": {},
"outputs": [],
"source": [
"# Run your code here"
]
},
{
"cell_type": "markdown",
"id": "94fc76cf",
"metadata": {},
"source": [
"Like before, in order to be able to inspect the p-values of the entire model and of each independent variable, we need to make use of `summary`:"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "37ce9c2b",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Call:\n",
"lm(formula = parent.grump ~ parent.sleep + baby.sleep, data = tutorial.dat)\n",
"\n",
"Residuals:\n",
" Min 1Q Median 3Q Max \n",
"-11.0345 -2.2198 -0.4016 2.6775 11.7496 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"(Intercept) 125.96557 3.04095 41.423 <2e-16 ***\n",
"parent.sleep -8.95025 0.55346 -16.172 <2e-16 ***\n",
"baby.sleep 0.01052 0.27106 0.039 0.969 \n",
"---\n",
"Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
"\n",
"Residual standard error: 4.354 on 97 degrees of freedom\n",
"Multiple R-squared: 0.8161,\tAdjusted R-squared: 0.8123 \n",
"F-statistic: 215.2 on 2 and 97 DF, p-value: < 2.2e-16\n",
"\n"
]
}
],
"source": [
"reg.model.2.summary<-summary( reg.model.2 )\n",
"print(reg.model.2.summary)"
]
},
{
"cell_type": "markdown",
"id": "0b5b0f1d",
"metadata": {},
"source": [
"As we can see, running this function on our regression object gives us several outputs:"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "4bdf45f9",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"
- 'call'
- 'terms'
- 'residuals'
- 'coefficients'
- 'aliased'
- 'sigma'
- 'df'
- 'r.squared'
- 'adj.r.squared'
- 'fstatistic'
- 'cov.unscaled'
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 'call'\n",
"\\item 'terms'\n",
"\\item 'residuals'\n",
"\\item 'coefficients'\n",
"\\item 'aliased'\n",
"\\item 'sigma'\n",
"\\item 'df'\n",
"\\item 'r.squared'\n",
"\\item 'adj.r.squared'\n",
"\\item 'fstatistic'\n",
"\\item 'cov.unscaled'\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 'call'\n",
"2. 'terms'\n",
"3. 'residuals'\n",
"4. 'coefficients'\n",
"5. 'aliased'\n",
"6. 'sigma'\n",
"7. 'df'\n",
"8. 'r.squared'\n",
"9. 'adj.r.squared'\n",
"10. 'fstatistic'\n",
"11. 'cov.unscaled'\n",
"\n",
"\n"
],
"text/plain": [
" [1] \"call\" \"terms\" \"residuals\" \"coefficients\" \n",
" [5] \"aliased\" \"sigma\" \"df\" \"r.squared\" \n",
" [9] \"adj.r.squared\" \"fstatistic\" \"cov.unscaled\" "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"names(reg.model.2.summary)"
]
},
{
"cell_type": "markdown",
"id": "286ccfbe",
"metadata": {},
"source": [
"One particularly important output has to do with the residuals. We can access this information by printing out the summary object or by using the residuals variable in that same object, as follows:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "07099660",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" Min. 1st Qu. Median Mean 3rd Qu. Max. \n",
"-11.0345 -2.2198 -0.4016 0.0000 2.6775 11.7496 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"summary(reg.model.2.summary$residuals)"
]
},
{
"cell_type": "markdown",
"id": "f9138602",
"metadata": {},
"source": [
"This output allows us to quickly check if the model is okay in terms of one of the assumptions of regression: that the residuals should be normally distributed with a mean of zero. Here, we see that the median is close to zero and the first and third quartiles are similar, indicating that normality is being satisfied (we'll come back to this in a more thorough way later though). "
]
},
{
"cell_type": "markdown",
"id": "bb534122",
"metadata": {},
"source": [
"A second important information is the part regarding the coefficients of the regression model. Let's inspect this accessing the variable \"coefficients\" in the summary object of our regression model:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "2730f629",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
\n",
"A matrix: 3 × 4 of type dbl\n",
"\n",
"\t | Estimate | Std. Error | t value | Pr(>|t|) |
|---|
\n",
"\n",
"\n",
"\t| (Intercept) | 125.96556586 | 3.0409482 | 41.42312073 | 1.764888e-63 |
|---|
\n",
"\t| parent.sleep | -8.95024973 | 0.5534577 | -16.17151638 | 2.747754e-29 |
|---|
\n",
"\t| baby.sleep | 0.01052447 | 0.2710637 | 0.03882656 | 9.691085e-01 |
|---|
\n",
"\n",
"
\n"
],
"text/latex": [
"A matrix: 3 × 4 of type dbl\n",
"\\begin{tabular}{r|llll}\n",
" & Estimate & Std. Error & t value & Pr(>\\textbar{}t\\textbar{})\\\\\n",
"\\hline\n",
"\t(Intercept) & 125.96556586 & 3.0409482 & 41.42312073 & 1.764888e-63\\\\\n",
"\tparent.sleep & -8.95024973 & 0.5534577 & -16.17151638 & 2.747754e-29\\\\\n",
"\tbaby.sleep & 0.01052447 & 0.2710637 & 0.03882656 & 9.691085e-01\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A matrix: 3 × 4 of type dbl\n",
"\n",
"| | Estimate | Std. Error | t value | Pr(>|t|) |\n",
"|---|---|---|---|---|\n",
"| (Intercept) | 125.96556586 | 3.0409482 | 41.42312073 | 1.764888e-63 |\n",
"| parent.sleep | -8.95024973 | 0.5534577 | -16.17151638 | 2.747754e-29 |\n",
"| baby.sleep | 0.01052447 | 0.2710637 | 0.03882656 | 9.691085e-01 |\n",
"\n"
],
"text/plain": [
" Estimate Std. Error t value Pr(>|t|) \n",
"(Intercept) 125.96556586 3.0409482 41.42312073 1.764888e-63\n",
"parent.sleep -8.95024973 0.5534577 -16.17151638 2.747754e-29\n",
"baby.sleep 0.01052447 0.2710637 0.03882656 9.691085e-01"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"reg.model.2.summary$coefficients"
]
},
{
"cell_type": "markdown",
"id": "a769fe20",
"metadata": {},
"source": [
"Each row in this table refers to one of the coefficients in the regression model, with the first row being the\n",
"intercept term, and the rest each of the independent varibles. \n",
"\n",
"Each column in this table gives us a particular information about each regression coefficient. The first column gives us the actual estimate, the second one gives uus the standard error of the estimate, the third column the t-statistic (i.e. the estimate/standard error), and the fourth column the p-value (without any correction; remember that this is like a post-hoc analys and therefore, we may need to adjust for testing multiple times...)."
]
},
{
"cell_type": "markdown",
"id": "8b120649",
"metadata": {},
"source": [
"We can also access the performance of the model, $R^2$, the adjusted performance and the F-statistic for the entire model:"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "cf2d437e",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"0.816105577097451"
],
"text/latex": [
"0.816105577097451"
],
"text/markdown": [
"0.816105577097451"
],
"text/plain": [
"[1] 0.8161056"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"0.812313939511832"
],
"text/latex": [
"0.812313939511832"
],
"text/markdown": [
"0.812313939511832"
],
"text/plain": [
"[1] 0.8123139"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"
- value
- 215.238286536844
- numdf
- 2
- dendf
- 97
\n"
],
"text/latex": [
"\\begin{description*}\n",
"\\item[value] 215.238286536844\n",
"\\item[numdf] 2\n",
"\\item[dendf] 97\n",
"\\end{description*}\n"
],
"text/markdown": [
"value\n",
": 215.238286536844numdf\n",
": 2dendf\n",
": 97\n",
"\n"
],
"text/plain": [
" value numdf dendf \n",
"215.2383 2.0000 97.0000 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"reg.model.2.summary$r.squared # R2\n",
"reg.model.2.summary$adj.r.squared # adjusted R2\n",
"reg.model.2.summary$fstatistic # F-statistic"
]
},
{
"cell_type": "markdown",
"id": "230d1b23",
"metadata": {},
"source": [
"
Practice question: Compute the F-statistic and the p-value for the entire model explicitly. For this, you will need to first compute $SS_{res}$, defined as $SS_{res}=\\sum_{i=1}^N(Y_i - \\hat{Y}_i)^2$, and $SS_{tot}$, defined as $SS_{tot}= \\sum_{i=1}^N(Y_i -
)^2$. (Hint: you can get $\\hat{Y}$ as the \"fitted.values\" in our regression model object, i.e. the one from running lm and that we have passed to summary.)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "92b8b6a1",
"metadata": {},
"outputs": [],
"source": [
"# Run your code here"
]
},
{
"cell_type": "markdown",
"id": "d015d856",
"metadata": {},
"source": [
"## Confidence intervals"
]
},
{
"cell_type": "markdown",
"id": "5cbc7d13",
"metadata": {},
"source": [
"The final thing we can try to calculate is the **confidence intervals** for our $\\beta$ estimates. These are not directly calculated when we run the regression model; instead, we may use the `confint` R built-in function:"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "4e131ebd",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"function (object, parm, level = 0.95, ...) \n",
"NULL
"
],
"text/latex": [
"\\begin{minted}{r}\n",
"function (object, parm, level = 0.95, ...) \n",
"NULL\n",
"\\end{minted}"
],
"text/markdown": [
"```r\n",
"function (object, parm, level = 0.95, ...) \n",
"NULL\n",
"```"
],
"text/plain": [
"function (object, parm, level = 0.95, ...) \n",
"NULL"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"?confint\n",
"args(confint)"
]
},
{
"cell_type": "markdown",
"id": "d136bd5e",
"metadata": {},
"source": [
"The only thing that we need to do is to pass the object containing the estimation of our regression model (i.e. the resulting object from using `lm`), and specify the level of confidence interval."
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "ef79812d",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A matrix: 3 × 2 of type dbl\n",
"\n",
"\t | 2.5 % | 97.5 % |
|---|
\n",
"\n",
"\n",
"\t| (Intercept) | 119.930125 | 132.0010063 |
|---|
\n",
"\t| parent.sleep | -10.048710 | -7.8517895 |
|---|
\n",
"\t| baby.sleep | -0.527462 | 0.5485109 |
|---|
\n",
"\n",
"
\n"
],
"text/latex": [
"A matrix: 3 × 2 of type dbl\n",
"\\begin{tabular}{r|ll}\n",
" & 2.5 \\% & 97.5 \\%\\\\\n",
"\\hline\n",
"\t(Intercept) & 119.930125 & 132.0010063\\\\\n",
"\tparent.sleep & -10.048710 & -7.8517895\\\\\n",
"\tbaby.sleep & -0.527462 & 0.5485109\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A matrix: 3 × 2 of type dbl\n",
"\n",
"| | 2.5 % | 97.5 % |\n",
"|---|---|---|\n",
"| (Intercept) | 119.930125 | 132.0010063 |\n",
"| parent.sleep | -10.048710 | -7.8517895 |\n",
"| baby.sleep | -0.527462 | 0.5485109 |\n",
"\n"
],
"text/plain": [
" 2.5 % 97.5 % \n",
"(Intercept) 119.930125 132.0010063\n",
"parent.sleep -10.048710 -7.8517895\n",
"baby.sleep -0.527462 0.5485109"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"confint( object = reg.model.2,level = .95)"
]
},
{
"cell_type": "markdown",
"id": "a9967e3a",
"metadata": {},
"source": [
"This will give us the confidence intervals for all the coefficients of our model. Alternatively, we could specify a subset of coefficients as well:"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "8afc8b12",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A matrix: 2 × 2 of type dbl\n",
"\n",
"\t | 2.5 % | 97.5 % |
|---|
\n",
"\n",
"\n",
"\t| parent.sleep | -10.048710 | -7.8517895 |
|---|
\n",
"\t| baby.sleep | -0.527462 | 0.5485109 |
|---|
\n",
"\n",
"
\n"
],
"text/latex": [
"A matrix: 2 × 2 of type dbl\n",
"\\begin{tabular}{r|ll}\n",
" & 2.5 \\% & 97.5 \\%\\\\\n",
"\\hline\n",
"\tparent.sleep & -10.048710 & -7.8517895\\\\\n",
"\tbaby.sleep & -0.527462 & 0.5485109\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A matrix: 2 × 2 of type dbl\n",
"\n",
"| | 2.5 % | 97.5 % |\n",
"|---|---|---|\n",
"| parent.sleep | -10.048710 | -7.8517895 |\n",
"| baby.sleep | -0.527462 | 0.5485109 |\n",
"\n"
],
"text/plain": [
" 2.5 % 97.5 % \n",
"parent.sleep -10.048710 -7.8517895\n",
"baby.sleep -0.527462 0.5485109"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"confint( object = reg.model.2, parm = c(\"parent.sleep\",\"baby.sleep\"), level = .95)"
]
},
{
"cell_type": "markdown",
"id": "9cfe67fa",
"metadata": {},
"source": [
"As we can see, at the 95% confidence level, the coefficient for parent.sleep does not include the value of zero, whereas the coefficient for baby.sleep does include it. That's why the former was found to be significant at this significance level, while the latter was not..."
]
},
{
"cell_type": "markdown",
"id": "cc8311ad",
"metadata": {},
"source": [
"## Working with categorical data\n",
"\n",
"Many variables of interest are usually categorical, such as gender, race, or personality type. In order to include these variables in a regression model, they must first be transformed into numerical variables. Dummy variable encoding is one of the different techniques used to achieve this transformation.\n",
"\n",
"Dummy variables take on a value of 0 or 1, indicating whether the observation belongs to a particular category or not. By including these dummy variables in the regression model, we can estimate the effect of each category on the dependent variable. \n",
"\n",
"Importantly, when creating dummy variables from a categorical variable, one of the categories need to be a BASELINE. The baseline category is the category against which all other categories are compared. Whenever we work with categorical variables in regression models, we need a baseline so that we can quantify how a change between categories is expected to affect the dependent variable. Similarly, a baseline is needed when having an intercept, since this cofficient captures the variability of Y when all X are equal to 0. A value 0 in the categorical variables needs to correspond to one particular category, which would be the baseline.\n",
"\n",
"In R, this is done automatically when including categorical variable in the regression model. \n",
"\n",
"Let's see this by creating a categorical variable in our dataset, \"day.cat\", corresponding to discretizing in 4 categories the days each observation was measured."
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "fa44b5f4",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A data.frame: 6 × 5\n",
"\n",
"\t | parent.sleep | baby.sleep | parent.grump | day | day.cat |
|---|
\n",
"\t | <dbl> | <dbl> | <int> | <int> | <fct> |
|---|
\n",
"\n",
"\n",
"\t| 1 | 7.59 | 10.18 | 56 | 1 | t0 |
|---|
\n",
"\t| 2 | 7.91 | 11.66 | 60 | 2 | t0 |
|---|
\n",
"\t| 3 | 5.14 | 7.92 | 82 | 3 | t0 |
|---|
\n",
"\t| 4 | 7.71 | 9.61 | 55 | 4 | t0 |
|---|
\n",
"\t| 5 | 6.68 | 9.75 | 67 | 5 | t0 |
|---|
\n",
"\t| 6 | 5.99 | 5.04 | 72 | 6 | t0 |
|---|
\n",
"\n",
"
\n"
],
"text/latex": [
"A data.frame: 6 × 5\n",
"\\begin{tabular}{r|lllll}\n",
" & parent.sleep & baby.sleep & parent.grump & day & day.cat\\\\\n",
" & & & & & \\\\\n",
"\\hline\n",
"\t1 & 7.59 & 10.18 & 56 & 1 & t0\\\\\n",
"\t2 & 7.91 & 11.66 & 60 & 2 & t0\\\\\n",
"\t3 & 5.14 & 7.92 & 82 & 3 & t0\\\\\n",
"\t4 & 7.71 & 9.61 & 55 & 4 & t0\\\\\n",
"\t5 & 6.68 & 9.75 & 67 & 5 & t0\\\\\n",
"\t6 & 5.99 & 5.04 & 72 & 6 & t0\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A data.frame: 6 × 5\n",
"\n",
"| | parent.sleep <dbl> | baby.sleep <dbl> | parent.grump <int> | day <int> | day.cat <fct> |\n",
"|---|---|---|---|---|---|\n",
"| 1 | 7.59 | 10.18 | 56 | 1 | t0 |\n",
"| 2 | 7.91 | 11.66 | 60 | 2 | t0 |\n",
"| 3 | 5.14 | 7.92 | 82 | 3 | t0 |\n",
"| 4 | 7.71 | 9.61 | 55 | 4 | t0 |\n",
"| 5 | 6.68 | 9.75 | 67 | 5 | t0 |\n",
"| 6 | 5.99 | 5.04 | 72 | 6 | t0 |\n",
"\n"
],
"text/plain": [
" parent.sleep baby.sleep parent.grump day day.cat\n",
"1 7.59 10.18 56 1 t0 \n",
"2 7.91 11.66 60 2 t0 \n",
"3 5.14 7.92 82 3 t0 \n",
"4 7.71 9.61 55 4 t0 \n",
"5 6.68 9.75 67 5 t0 \n",
"6 5.99 5.04 72 6 t0 "
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"\n",
"t0 t1 t2 t3 \n",
"25 25 25 25 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tutorial.dat.cat<-tutorial.dat %>% mutate(day.cat = cut(day, breaks = c(0, 25, 50, 75, 100), \n",
" labels = c(\"t0\", \"t1\", \"t2\", \"t3\")))\n",
"\n",
"head(tutorial.dat.cat)\n",
"table(tutorial.dat.cat$day.cat)"
]
},
{
"cell_type": "markdown",
"id": "4534ac4b",
"metadata": {},
"source": [
"And see what hapeens when we include \"day.cat\" as an independent variablem in the regression model:"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "1cc31f51",
"metadata": {},
"outputs": [],
"source": [
"reg.model.cat<-lm(parent.grump~parent.sleep + baby.sleep + day.cat, \n",
" data=tutorial.dat.cat)"
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "a06ccc06",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"lm(formula = parent.grump ~ parent.sleep + baby.sleep + day.cat, \n",
" data = tutorial.dat.cat)\n",
"\n",
"Coefficients:\n",
" (Intercept) parent.sleep baby.sleep day.catt1 day.catt2 \n",
" 126.10800 -8.83376 -0.04098 -1.53248 -0.26295 \n",
" day.catt3 \n",
" -0.36150 \n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"reg.model.cat"
]
},
{
"cell_type": "markdown",
"id": "be9336b0",
"metadata": {},
"source": [
"Now we have an estimated cofficient for every single category but one, because as we said, one of the categories is always used as a baseline. \n",
"\n",
"If we pass this estimated regression object, we can get the p-values for each coefficient:"
]
},
{
"cell_type": "code",
"execution_count": 32,
"id": "8bb18d87",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"lm(formula = parent.grump ~ parent.sleep + baby.sleep + day.cat, \n",
" data = tutorial.dat.cat)\n",
"\n",
"Residuals:\n",
" Min 1Q Median 3Q Max \n",
"-11.1618 -2.5089 -0.4761 2.7700 11.5339 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"(Intercept) 126.10800 3.20003 39.408 <2e-16 ***\n",
"parent.sleep -8.83376 0.57152 -15.457 <2e-16 ***\n",
"baby.sleep -0.04098 0.27685 -0.148 0.883 \n",
"day.catt1 -1.53248 1.24901 -1.227 0.223 \n",
"day.catt2 -0.26295 1.24625 -0.211 0.833 \n",
"day.catt3 -0.36150 1.24662 -0.290 0.772 \n",
"---\n",
"Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
"\n",
"Residual standard error: 4.382 on 94 degrees of freedom\n",
"Multiple R-squared: 0.8195,\tAdjusted R-squared: 0.8099 \n",
"F-statistic: 85.34 on 5 and 94 DF, p-value: < 2.2e-16\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"summary( reg.model.cat )"
]
},
{
"cell_type": "markdown",
"id": "4fdd27d6",
"metadata": {},
"source": [
"Looking at these p-values, there appear to be no statistical differences in grumpiness between different day epochs."
]
},
{
"cell_type": "markdown",
"id": "24db835a",
"metadata": {},
"source": [
"# CHECKING OUR REGRESSION MODEL\n",
"\n",
"\n",
"Ok, so we've just seen how to estimate our regression model and make inferences on it. But were we correct in using such a model to describe the relationship between our dependent variable and the independent variables? We need to make sure that the assumptions of the regression model are satisfied to a certain degree. Let's have a look at how to check this in R:"
]
},
{
"cell_type": "markdown",
"id": "b92029ba",
"metadata": {},
"source": [
"## 1. Linearity\n",
"\n",
"The first thing we can check is whether there exists a linear relation between the independent variables and dependent variable. We will address this assumption using a *Residuals vs Fitted* plot, such that if the residuals are uniformly distributed around a horizontal line with no noticeable patterns, this suggests a strong possibility of a linear relationship.\n",
"\n",
"In R we can accomplish this just by passing our regression model object to the `plot` function and setting the argument \"which\" equal 1:"
]
},
{
"cell_type": "code",
"execution_count": 33,
"id": "2a0e9782",
"metadata": {},
"outputs": [
{
"data": {
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KAJFDsAAAAAmkCxAwAAAKAJFDsAAAAA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pFByRiGdQceSvtwzxNKpof7RmqqqqOTk5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\n+IYdIYQQQmiUwMYOIYQQQmiU+AedZwo38qCiUAAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title “”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot(reg.model.2, which=1)"
]
},
{
"cell_type": "markdown",
"id": "aa00493b",
"metadata": {},
"source": [
"As we can see, this plot not only does draws the scatter plot showing the fitted value against the residuals, but also a line that shows the relationship between the fitted values and the residuals. Ideally, this relationship should be a straight, perfectly horizontal line. Here we see a bit of curvature, but it seems quite mild, so we should worry too much about it."
]
},
{
"cell_type": "markdown",
"id": "30a51f1c",
"metadata": {},
"source": [
"## 2. Normality of the residuals\n",
"\n",
"We saw in previous tutorials how to test the normality of the data. Here we should apply that knowledge to the **residuals**. Remember that we can always get the residuals in our regression model object by accessing its variable named \"residuals\"."
]
},
{
"cell_type": "code",
"execution_count": 34,
"id": "dcf50578",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAA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\nAIAj/gccxcupqsI/WwAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title “Histogram of reg.model.2$residuals”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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2XvNWi3U7ddmpUUfiEHv7/Zhh8MAID1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\nAAAAAElFTkSuQmCC",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"# Visually using histograms\n",
"hist(x=reg.model.2$residuals, breaks=10)\n",
"ggplot() + geom_histogram(mapping = aes(x=reg.model.2$residuals), bins=12, color='black',fill=\"grey\") + theme_classic()"
]
},
{
"cell_type": "markdown",
"id": "06948b04",
"metadata": {},
"source": [
"We can more efficiently look at this by making a Q-Q plot. We could use **ggplot** as we studied, or more quickly using the `plot` function and setting the argument \"which\" equal 2:"
]
},
{
"cell_type": "code",
"execution_count": 35,
"id": "4c8ef3d4",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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Xuvivqer/e9ePHi2rVrL126JIRwc3Pr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\nAABQjeEfdgAAAACOQGEHAAAAwBH/B8d0fNJ8glCmAAAAAElFTkSuQmCC",
"text/plain": [
"Plot with title “”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot(reg.model.2, which=2)"
]
},
{
"cell_type": "markdown",
"id": "84cdda0b",
"metadata": {},
"source": [
"As we can see, residuals appear to follow a gaussian distribution. To be even more sure, we could try to address this statistically by running a Shapiro-Wilk test:"
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "ac9362da",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"\tShapiro-Wilk normality test\n",
"\n",
"data: reg.model.2$residuals\n",
"W = 0.99228, p-value = 0.8414\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Statistically\n",
"shapiro.test(reg.model.2$residuals)"
]
},
{
"cell_type": "markdown",
"id": "556d7b5e",
"metadata": {},
"source": [
"So yeah, as we suspected, our regression model appears to satisfy the condition on normality of the residulas."
]
},
{
"cell_type": "markdown",
"id": "805594ab",
"metadata": {},
"source": [
"## 3. Varience homogeneity of the residuals\n",
"\n",
"Here again we turn our attention to the residuals to see if their variance are more or less constant. In order to check this condition, we will utilize a *Scale-Location* plot, also known as a spread-location plot, which displays the square root of the absolute standardized residuals (or studentized residuals) against the fitted values of the dependent variable. If the variance of the residuals is constant across all fitted values, the points in the plot will be randomly scattered around a horizontal line at a constant distance from zero. However, if there is a pattern or trend in the plot, it may suggest that the variance of the residuals is not constant, and that the assumptions of homogeneit of variance (also called homoscedasticity) may have been violated.\n",
"\n",
"In R, this kind of plots can be easily achieved using the `plot` function and setting the argument \"which\" equal 3:"
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "7a8d6745",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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4OHJ4DhpKWlCwoKmtz06dMnWVlZHucBYJLVq1ffuHHj6dOnxsbGdcN9+/b5+/sb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\njaVSZBwHywyzIRl1o10rZs6c+fTp06FDhwYEBDS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tbe2yZct++eWX8+fPSyc/6ng83r59++zt7el0utqvUagAACAASURBVLq6uoeHx61b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\npWms4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"text/plain": [
"Plot with title “”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot(reg.model.2, which=3)"
]
},
{
"cell_type": "markdown",
"id": "a4b64c8b",
"metadata": {},
"source": [
"As we can see here, our line is almost straight and flat, suggesting that indeed our residuals have a constant variance."
]
},
{
"cell_type": "markdown",
"id": "0c2d3703",
"metadata": {},
"source": [
"## 4. No extreme outliers\n",
"\n",
"Here we have two options to check this condition. The first one involves making use of the so-called *Cook's distance*, which is a measure of the influence of individual data points on the regression coefficients in a regression model. It calculates the change in the regression coefficients when a particular observation is deleted from the dataset, so it measures how much the regression coefficients would change if the observation were to be excluded from the analysis. A large value of Cook's distance for a given observation suggests that the observation has a large influence on the regression coefficients and may be an outlier or influential point that should be examined more closely. Cook's distance values range from 0 to 1, with larger values indicating greater influence of the observation on the regression coefficients. Generally, a threshold value of 1 is used to identify influential observations.\n",
"\n",
"\n",
"In R, we can generate a plot for the Cook's distances of each observation by means of the `plot` function and setting the argument \"which\" equal 4:"
]
},
{
"cell_type": "code",
"execution_count": 38,
"id": "c76ab229",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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Aqha8VOXZBf8NhzebdTU1Oz8ssyDwAA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\nGhlUSfQ8enw7uG5Z5AQAAIAGGovdiZgYtXHn8d+F1XGxrdYiyC1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5UOzkicykuw804/5OvHb1aqZ/z+GttLm7hKr6yOXzT4X0Wzy45eLh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",
"text/plain": [
"Plot with title “”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot(reg.model.2, which=4)"
]
},
{
"cell_type": "markdown",
"id": "f5f8a6a6",
"metadata": {},
"source": [
"And alternative method for identifying outliers is by means of a *Residuals vs Leverage* plot, which displays the standardized residuals (or studentized residuals) against the leverage values of the observations. Leverage values are a measure of how much an observation deviates from the average value of the predictor variables. \n",
"\n",
"Large leverage observations are those that have extreme values on one or more predictor variables. In general, observations with large leverage values and large residuals are of greater concern because they have the potential to exert a strong influence on the regression coefficients. If an observation has both a large leverage value and a large residual, it can be considered an influential point that should be examined more closely. Conversely, if an observation has a low leverage value and a small residual, it can be considered a low-influence point that is unlikely to have a significant impact on the regression coefficients.\n",
"\n",
"In R we can plot this by means of the `plot` function and setting the argument \"which\" equal 5:"
]
},
{
"cell_type": "code",
"execution_count": 39,
"id": "477c910d",
"metadata": {},
"outputs": [
{
"data": {
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ExQ7OiG4QkAAAAQExQ7umF4AgAAAMQE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\n/g+/27Wutg1dRgAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title “”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot(reg.model.2, which=5)"
]
},
{
"cell_type": "markdown",
"id": "4a1ce010",
"metadata": {},
"source": [
"As we can see, both plots suggest a few points as possible outliers. Are these so? The quickets way of checking this is by running the regression with every outlier candidate excluded and see what happens to the model performance and to the regression coefficients. If they really are substantially different, we may to need to take that observation into further consideration. If we believe this observation was not supposed to be there and is badly distorting our results, we might consider excluding it.\n",
"\n",
"How can we rerun our regression models excluding a particular observation? Well, the `lm` function has the argument \"subset\" that allows us to do that. Let's see this, separately, for the points 64 and 85 of our dataset:"
]
},
{
"cell_type": "code",
"execution_count": 41,
"id": "07555931",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"lm(formula = parent.grump ~ parent.sleep + baby.sleep, data = tutorial.dat, \n",
" subset = -64)\n",
"\n",
"Coefficients:\n",
" (Intercept) parent.sleep baby.sleep \n",
" 126.3553 -8.8283 -0.1319 \n"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"lm(formula = parent.grump ~ parent.sleep + baby.sleep, data = tutorial.dat, \n",
" subset = -85)\n",
"\n",
"Coefficients:\n",
" (Intercept) parent.sleep baby.sleep \n",
" 124.50234 -8.69714 -0.03846 \n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lm( formula = parent.grump ~ parent.sleep + baby.sleep, # same formula\n",
"data = tutorial.dat, # same data frame...\n",
"subset = -64)\n",
"\n",
"lm( formula = parent.grump ~ parent.sleep + baby.sleep, # same formula\n",
"data = tutorial.dat, # same data frame...\n",
"subset = -85)"
]
},
{
"cell_type": "markdown",
"id": "0bcffbac",
"metadata": {},
"source": [
"As we can see, in both cases the regression coefficients barely change in comparison to the values using the full dataset, so we can infer that these points are no problem."
]
},
{
"cell_type": "markdown",
"id": "a4843b9f",
"metadata": {},
"source": [
"## 5- Independent residuals\n",
"\n",
"To check this assumption, we will create an ACF plot, which a commonly used diagnostic tool to check for correlations between residuals (i.e. also known as autocorrelations) in regression analysis. An autocorrelation is a measure of the degree of similarity between a series of observations and a delayed version of itself. In the case of the residuals, if these are independent, then the autocorrelation coefficients should not be significantly different from zero for all lags. On the other hand, if there is significant autocorrelation in the residuals, it suggests that there is still some pattern or structure in the data that is not captured by the regression model. This can result in biased or inefficient parameter estimates and can affect the accuracy and reliability of the model's predictions.\n",
"\n",
"An ACF plot to test the independence of the residuals is created by plotting the residuals against their own lagged values. If the ACF plot shows that the autocorrelation coefficients are not significantly different from zero for all lags, then it suggests that the residuals are independent and that the regression model is appropriate for the data. However, if there are significant autocorrelation coefficients at certain lags, then this suggests that the residuals are not independent and that the regression model may need to be revised or improved.\n",
"\n",
"In R, this kind of plots can be generated using the `acf` function as follows:"
]
},
{
"cell_type": "code",
"execution_count": 49,
"id": "b796c9a9",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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/mfsV99N6sP33UCAABeVDoSdkIIQ8dXBn74ysB8t1i1mhByfmzCv5FR8QZ2NWva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\nFEGwAwAAUMT/A6a7G9MzZdZCAAAAAElFTkSuQmCC",
"text/plain": [
"Plot with title “Series reg.model.2$residuals”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"acf(reg.model.2$residuals, type = \"correlation\")"
]
},
{
"cell_type": "markdown",
"id": "a59366e4",
"metadata": {},
"source": [
"We need to omit the first value in this graph (Lag=0) because it corresponds to the correlation of each variable with itself, which is always 1. As we can see in this plot, all autocorrelations from the residuals are small, indicating independence between them."
]
},
{
"cell_type": "markdown",
"id": "891d2114",
"metadata": {},
"source": [
"# 6- No collinearity between the independent variables\n",
"\n",
"Maybe here the easiest way would be to compute the correlation matrix of the independent variables and search for large correlations between pairs of variables. This may indicate collinearity. How large? We would probably be talking about correlations of the order of 0.7 or greater. \n",
"\n",
"In order to calculate this matrix, we can use the `cor` function:"
]
},
{
"cell_type": "code",
"execution_count": 40,
"id": "359a33fd",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A matrix: 3 × 3 of type dbl\n",
"\n",
"\t | parent.sleep | baby.sleep | day |
|---|
\n",
"\n",
"\n",
"\t| parent.sleep | 1.00000000 | 0.62794934 | -0.09840768 |
|---|
\n",
"\t| baby.sleep | 0.62794934 | 1.00000000 | -0.01043394 |
|---|
\n",
"\t| day | -0.09840768 | -0.01043394 | 1.00000000 |
|---|
\n",
"\n",
"
\n"
],
"text/latex": [
"A matrix: 3 × 3 of type dbl\n",
"\\begin{tabular}{r|lll}\n",
" & parent.sleep & baby.sleep & day\\\\\n",
"\\hline\n",
"\tparent.sleep & 1.00000000 & 0.62794934 & -0.09840768\\\\\n",
"\tbaby.sleep & 0.62794934 & 1.00000000 & -0.01043394\\\\\n",
"\tday & -0.09840768 & -0.01043394 & 1.00000000\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A matrix: 3 × 3 of type dbl\n",
"\n",
"| | parent.sleep | baby.sleep | day |\n",
"|---|---|---|---|\n",
"| parent.sleep | 1.00000000 | 0.62794934 | -0.09840768 |\n",
"| baby.sleep | 0.62794934 | 1.00000000 | -0.01043394 |\n",
"| day | -0.09840768 | -0.01043394 | 1.00000000 |\n",
"\n"
],
"text/plain": [
" parent.sleep baby.sleep day \n",
"parent.sleep 1.00000000 0.62794934 -0.09840768\n",
"baby.sleep 0.62794934 1.00000000 -0.01043394\n",
"day -0.09840768 -0.01043394 1.00000000"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Just dropping the dependent variable\n",
"cor(tutorial.dat %>% select(!parent.grump))"
]
},
{
"cell_type": "markdown",
"id": "4d2a048f",
"metadata": {},
"source": [
"As we can see, the variables \"baby.sleep\" and \"parent.sleep\" are correlated, but not at the level of being super super large, so we could assume that collinearity is not a problem here.\n",
"\n",
"Let's see a case where this might indeed be a problem. As we saw before, the amount of time slept by the parent, i.e. \"parent.sleep\", is highly associated with their grumpiness, i.e. \"parent.grump\". In fact, there was a really large correlation between them:"
]
},
{
"cell_type": "code",
"execution_count": 41,
"id": "5f6a2f49",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"\tPearson's product-moment correlation\n",
"\n",
"data: tutorial.dat$parent.sleep and tutorial.dat$parent.grump\n",
"t = -20.854, df = 98, p-value < 2.2e-16\n",
"alternative hypothesis: true correlation is not equal to 0\n",
"95 percent confidence interval:\n",
" -0.9340614 -0.8594714\n",
"sample estimates:\n",
" cor \n",
"-0.903384 \n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cor.test(tutorial.dat$parent.sleep, tutorial.dat$parent.grump)"
]
},
{
"cell_type": "markdown",
"id": "4941c28b",
"metadata": {},
"source": [
"What happens if we use these two highly correlated variables as independent variables in the same model? Let's see what happens if we do this:"
]
},
{
"cell_type": "code",
"execution_count": 42,
"id": "daf12022",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"lm(formula = baby.sleep ~ parent.sleep + parent.grump, data = tutorial.dat)\n",
"\n",
"Residuals:\n",
" Min 1Q Median 3Q Max \n",
"-3.9335 -1.3232 -0.0077 1.0108 4.2341 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"(Intercept) -1.067200 4.923129 -0.217 0.828841 \n",
"parent.sleep 1.295343 0.376234 3.443 0.000851 ***\n",
"parent.grump 0.001477 0.038032 0.039 0.969108 \n",
"---\n",
"Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
"\n",
"Residual standard error: 1.631 on 97 degrees of freedom\n",
"Multiple R-squared: 0.3943,\tAdjusted R-squared: 0.3818 \n",
"F-statistic: 31.58 on 2 and 97 DF, p-value: 2.744e-11\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"summary(lm(baby.sleep ~ parent.sleep + parent.grump, data=tutorial.dat))"
]
},
{
"cell_type": "markdown",
"id": "c349a89e",
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"source": [
"Now, let's run the same model but replacing \"parent.grump\" with the variable \"day\", which was not correlated with the amount of time slept by the parent."
]
},
{
"cell_type": "code",
"execution_count": 43,
"id": "e7416e5f",
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{
"data": {
"text/plain": [
"\n",
"Call:\n",
"lm(formula = baby.sleep ~ parent.sleep + day, data = tutorial.dat)\n",
"\n",
"Residuals:\n",
" Min 1Q Median 3Q Max \n",
"-3.9894 -1.2543 -0.0376 1.0945 4.3915 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"(Intercept) -1.141046 1.200576 -0.950 0.344 \n",
"parent.sleep 1.292567 0.161772 7.990 2.82e-12 ***\n",
"day 0.003708 0.005665 0.655 0.514 \n",
"---\n",
"Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
"\n",
"Residual standard error: 1.627 on 97 degrees of freedom\n",
"Multiple R-squared: 0.397,\tAdjusted R-squared: 0.3846 \n",
"F-statistic: 31.93 on 2 and 97 DF, p-value: 2.218e-11\n"
]
},
"metadata": {},
"output_type": "display_data"
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],
"source": [
"summary(lm(baby.sleep ~ parent.sleep + day, data=tutorial.dat))"
]
},
{
"cell_type": "markdown",
"id": "f45de1ff",
"metadata": {},
"source": [
"As we can see, and turning our attention exclusively to the variable \"parent.sleep\", in both cases the estimated $\\beta$ coefficient for this variable is the same. What happens is that in the presence of collinearity, errors tend to be large, which is not a good idea both for inference, and for the stability of the model."
]
},
{
"cell_type": "markdown",
"id": "4c14b4a7",
"metadata": {},
"source": [
"**IMPORTANT:** In this section on checking the assumptions of the regression model, I tried to stick to methods that employ only R built-in functions. There are tons of packages that could allow you to investigate this question in a more thorough detail. For example, you could check the **car** and **lmtest** packages out. These provide you , among other things, with a non-constant variance test for checking statistically the homogeneity of variance of the residuals, a measure of collinearity called \"Variance Inflation Factor\" (VIF) and an implementation of the Durbin Watson Test for addressing statistically the possible dependence between residuals. You should definetely check all this out in the main textbook of the course, or on the internet for example."
]
}
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