Make sure to include the unit of the values whenever appropriate.

Q1 Build a regression model to predict wages using the following predictors: 1) years of education, 2) years of experience, and 3) sex.

Hint: The variables are available in the CPS85 data set from the mosaicData package.

data(CPS85, package="mosaicData")
wages_lm <- lm(wage ~ educ + exper + sex,
                data = CPS85)

# View summary of model 1
summary(wages_lm)
## 
## Call:
## lm(formula = wage ~ educ + exper + sex, data = CPS85)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -9.571 -2.746 -0.653  1.893 37.724 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -6.50451    1.20985  -5.376 1.14e-07 ***
## educ         0.94051    0.07886  11.926  < 2e-16 ***
## exper        0.11330    0.01671   6.781 3.19e-11 ***
## sexM         2.33763    0.38806   6.024 3.19e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.454 on 530 degrees of freedom
## Multiple R-squared:  0.2532, Adjusted R-squared:  0.2489 
## F-statistic: 59.88 on 3 and 530 DF,  p-value: < 2.2e-16

Q2 Is the coefficient of education statistically significant at 5%?

The coefficient of education is statisically significant at 5%.

Q3 Interpret the coefficient of education.

Hint: Discuss both its sign and magnitude.

This means that we are 99.9% confident that the intercept is true. This means that we are extremely confident that education has an impact on wages.

Q4 Is there evidence for gender discrimination in wages? Make your argument using the relevant test results.

Hint: Discuss all three aspects of the relevant predictor: 1) statistical significance, 2) sign, and 3) magnitude.

There is evidence for gender discrimination in wages. The coefficient of sex is statisctically significant in determining wages. The sign for the variable is positive and the magnitude is 2.33.

Q5 Predict wage for a woman who has 15 years of education, 5 years of experience.

The wage for a woman who has 15 years of education and 5 years of experience is $14.67.

Q6 Interpret the Intercept.

Hint: Provide a technical interpretation.

The intercept is -6.50451. This means that the base wage is $6.50 if all other intercepts are 0.

Q7 Build another model by adding a predictor to the model above. The additional predictor is whether the person is a union member. Which of the two models is better?

Hint: Discuss in terms of both residual standard error and reported adjusted R squared.

data(CPS85, package="mosaicData")
wages_lm <- lm(wage ~ educ + exper + sex + union,
                data = CPS85)

# View summary of model 1
summary(wages_lm)
## 
## Call:
## lm(formula = wage ~ educ + exper + sex + union, data = CPS85)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -9.496 -2.708 -0.712  1.909 37.784 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -6.48023    1.20159  -5.393 1.05e-07 ***
## educ         0.93495    0.07835  11.934  < 2e-16 ***
## exper        0.10692    0.01674   6.387 3.70e-10 ***
## sexM         2.14765    0.39097   5.493 6.14e-08 ***
## unionUnion   1.47111    0.50932   2.888  0.00403 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.423 on 529 degrees of freedom
## Multiple R-squared:  0.2648, Adjusted R-squared:  0.2592 
## F-statistic: 47.62 on 4 and 529 DF,  p-value: < 2.2e-16

The residual standard error for the first set of data is 4.454 and 4.423 for the second set. The error for the second data is lower and means that it misses the actual wage by less than the first data set.

The adjusted R-squared for the first data set is 0.2489 and 0.2592 for the second set. This means that 25% and 26% of the variability in wages is expressed in the models.

The second model misses the actual wage by less than the first model, and also shows more of the variability than the first model making the second model much better.

Q8 Hide the messages, but display the code and its results on the webpage.

Hint: Use message, echo and results in the chunk options. Refer to the RMarkdown Reference Guide.

Q9 Display the title and your name correctly at the top of the webpage.

Q10 Use the correct slug.