2.3 At-Home Exercises

2.3.1 Setup

To complete the following exercises, you’ll need to install the packages described in the following table.

Package Description
haven Loading data from SPSS ‘.sav’ files
tidySEM Plotting and tabulating the output of SEM-models

Use the install.packages() function to install these packages.

Click for explanation
  1. Open RStudio
  2. Inside RStudio, find the window named Console on left side of the screen.
  3. Copy the following code into the console and hit Enter/Return to run the command.
install.packages(c("haven", "tidySEM"), dependencies = TRUE)

2.3.2

Use the haven::read_spss() function to load the LifeSat.sav data.

Click for explanation 
library(dplyr)
library(haven)

LifeSat <- read_spss("LifeSat.sav")

2.3.3

Make a table of descriptive statistics for the variables: LifSat, educ, ChildSup, SpouSup, and age.

  • What is the average age in the sample?
  • What is the range (youngest and oldest child)?

Hint: Use the tidySEM::descriptives() function.`

Click for explanation
  • The package tidySEM contains the descriptives() function for computing descriptive statistics.
  • The describe() function in the psych package is a good alternative.
library(tidySEM)

descriptives(LifeSat[ , c("LifSat", "educ", "ChildSup", "SpouSup", "age")])

2.3.4

Run a simple linear regression with LifSat as the dependent variable and educ as the independent variable.

Hints:

  • The lm() function (short for linear model) does linear regression.
  • The summary() function provides relevant summary statistics for the model.
  • It can be helpful to store the results of your analysis in an object.
Click for explanation 
results <- lm(LifSat ~ educ, data = LifeSat)
summary(results)
## 
## Call:
## lm(formula = LifSat ~ educ, data = LifeSat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -43.781 -11.866   2.018  12.418  43.018 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   35.184      7.874   4.469 2.15e-05 ***
## educ           3.466      1.173   2.956  0.00392 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.64 on 96 degrees of freedom
## Multiple R-squared:  0.08344,    Adjusted R-squared:  0.0739 
## F-statistic:  8.74 on 1 and 96 DF,  p-value: 0.003918

2.3.5

Repeat the analysis from 2.3.4 with age as the independent variable.

Click for explanation 
results <- lm(LifSat ~ age, data = LifeSat)
summary(results)
## 
## Call:
## lm(formula = LifSat ~ age, data = LifeSat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -35.321 -14.184   3.192  13.593  40.626 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 200.2302    52.1385   3.840  0.00022 ***
## age          -2.0265     0.7417  -2.732  0.00749 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.75 on 96 degrees of freedom
## Multiple R-squared:  0.07215,    Adjusted R-squared:  0.06249 
## F-statistic: 7.465 on 1 and 96 DF,  p-value: 0.007487

2.3.6

Repeat the analysis from 2.3.4 and 2.3.5 with ChildSup as the independent variable.

Click for explanation 
results <- lm(LifSat ~ ChildSup, data = LifeSat)
summary(results)
## 
## Call:
## lm(formula = LifSat ~ ChildSup, data = LifeSat)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -37.32 -12.14   0.66  12.41  44.68 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   37.559      8.342   4.502 1.89e-05 ***
## ChildSup       2.960      1.188   2.492   0.0144 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.86 on 96 degrees of freedom
## Multiple R-squared:  0.06076,    Adjusted R-squared:  0.05098 
## F-statistic: 6.211 on 1 and 96 DF,  p-value: 0.01441

2.3.7

Run a multiple linear regression with LifSat as the dependent variable and educ, age, and ChildSup as the independent variables.

Hint: You can use the + sign to add multiple variables to the right hand side (RHS) of your model formula.

Click for explanation 
results <- lm(LifSat ~ educ + age + ChildSup, data = LifeSat)
summary(results)
## 
## Call:
## lm(formula = LifSat ~ educ + age + ChildSup, data = LifeSat)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -32.98 -12.56   2.68  11.03  41.91 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 134.9801    53.2798   2.533   0.0130 *
## educ          2.8171     1.1436   2.463   0.0156 *
## age          -1.5952     0.7188  -2.219   0.0289 *
## ChildSup      2.4092     1.1361   2.121   0.0366 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 16.92 on 94 degrees of freedom
## Multiple R-squared:  0.1741, Adjusted R-squared:  0.1477 
## F-statistic: 6.603 on 3 and 94 DF,  p-value: 0.0004254

2.3.8

Compare the results from 2.3.7 with those from 2.3.4, 2.3.5, and 2.3.6.

  • What do you notice when you compare the estimated slopes for each of the three predictors in the multiple regression model with the corresponding estimates from the simple regression models?

End of At-Home Exercises