Question

This question requires using Rstudio. This is following commands to install and import data into R:

> install.packages("ISLR")
> library(ISLR)
> data(Wage)

The required data installed and imported, now this is description of the data:

This dataset contains economic and demographic data for 3000 individuals living in the mid-Atlantic region. For each of the
3000 individuals, the following 11 variables are recorded:

year: Year that wage information was recorded
age: Age of worker
maritl: A factor with levels 1. Never Married 2. Married 3. Widowed 4. Divorced and 5.
Separated indicating marital status
race: A factor with levels 1. White 2. Black 3. Asian and 4. Other indicating race
education: A factor with levels 1. < HS Grad 2. HS Grad 3. Some College 4. College Grad
and 5. Advanced Degree indicating education level
region: Region of the country (mid-atlantic only)
jobclass: A factor with levels 1. Industrial and 2. Information indicating type of job
health: A factor with levels 1. <=Good and 2. >=Very Good indicating health level of worker
health ins: A factor with levels 1. Yes and 2. No indicating whether worker has health insurance
logwage: Log of workers wage
wage: Workers raw wage

This question continues with the Wage dataset.

You wish to fit a multiple regression model to predict wage using year, age, and jobclass.

However, you are interested in whether the change in wage as a worker ages differs between

industrial workers and information workers. Fit the appropriate model and test the

hypothesis of interest. Include your results and your conclusion.

Please provide all necessary codes using Rstudio.

Answer 1

library(ISLR)

data(Wage)

head(Wage)

       year age     sex           maritl     race       education             region       jobclass         health health_ins

231655 2006 18 1. Male 1. Never Married 1. White    1. < HS Grad 2. Middle Atlantic 1. Industrial      1. <=Good      2. No

86582 2004 24 1. Male 1. Never Married 1. White 4. College Grad 2. Middle Atlantic 2. Information 2. >=Very Good      2. No

161300 2003 45 1. Male       2. Married 1. White 3. Some College 2. Middle Atlantic 1. Industrial      1. <=Good     1. Yes

155159 2003 43 1. Male       2. Married 3. Asian 4. College Grad 2. Middle Atlantic 2. Information 2. >=Very Good     1. Yes

11443 2005 50 1. Male      4. Divorced 1. White      2. HS Grad 2. Middle Atlantic 2. Information      1. <=Good     1. Yes

376662 2008 54 1. Male       2. Married 1. White 4. College Grad 2. Middle Atlantic 2. Information 2. >=Very Good     1. Yes

        logwage      wage

231655 4.318063 75.04315

86582 4.255273 70.47602

161300 4.875061 130.98218

155159 5.041393 154.68529

11443 4.318063 75.04315

376662 4.845098 127.11574

regmodel <- lm(wage ~ year+age+jobclass, data = Wage)

summary(regmodel)

Call:

lm(formula = wage ~ year + age + jobclass, data = Wage)

Residuals:

     Min       1Q   Median       3Q      Max 

-103.646  -24.525   -6.118   16.406  200.662 

Coefficients:

                         Estimate Std. Error t value Pr(>|t|)    

(Intercept)            -2.400e+03  7.252e+02  -3.309 0.000946 ***

year                    1.235e+00  3.616e-01   3.415 0.000646 ***

age                     6.362e-01  6.373e-02   9.982  < 2e-16 ***

jobclass2. Information  1.597e+01  1.471e+00  10.859  < 2e-16 ***

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 40.09 on 2996 degrees of freedom

Multiple R-squared:  0.07794, Adjusted R-squared:  0.07702 

F-statistic: 84.41 on 3 and 2996 DF,  p-value: < 2.2e-16

Regression Equation

Wage = -2399.90 + 1.23 * year + 0.64 * age + 15.97 * jobclass2. Information

Null and Alternate Hypothesis

H₀: All the coefficients of the linear model are zero

H_a: Not all the coefficients of the linear model are zero

From the ANOVA table, since the p-value is less than 0.05, hence we reject the null hypothesis ie the model is significant ie not all coefficients are zero.

Also, the p-value for the independent variable is less than 0.05, hence the variable is significant ie there exists a relationship between the dependent and the independent variable.