2.3 At-Home Exercises

Load the LifeSat.sav data.

library(dplyr)
library(haven)

LifeSat <- read_spss("LifeSat.sav") 

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2.3.1

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")])

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2.3.2

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

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2.3.3

Repeat the analysis from 2.3.2 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

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2.3.4

Repeat the analysis from 2.3.2 and 2.3.3 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

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2.3.5

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

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2.3.6

Compare the results from 2.3.5 with those from 2.3.2, 2.3.3, and 2.3.4.

• 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?

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End of At-Home Exercises

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