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.

options(scipen=999)
data(CPS85, package="mosaicData")
wage_lm <- lm(wage ~ educ + exper + sex,
                data = CPS85)

# View summary of model 1
summary(wage_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      0.0000001141795 ***
## educ         0.94051    0.07886  11.926 < 0.0000000000000002 ***
## exper        0.11330    0.01671   6.781      0.0000000000319 ***
## sexM         2.33763    0.38806   6.024      0.0000000031877 ***
## ---
## 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: < 0.00000000000000022

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

Yes it is statistically significant at 5% because its P value is smaller than 0.05. Its P value is 0.0000000000000002, which means we are 99.9% confident that the intercept is true.

Q3 Interpret the coefficient of education.

For every year of education one completes, their wage will go up $0.94.

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

Yes, there is evidence for gender discrimination in wages because males make $2.33 more than females make in wages.

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

If a woman has 15 years of education and 5 years of experience, she should make $12.32 an hour. I took the 0.94 from the education predictor and multiplied it by 15 because for every year of education, the wage goes up 94 cents. After, I multiplied 0.11 (which is from the exper predictor) and multiplied it by 5 because she has 5 years of experience. I added the 2 numbers together and subtracted 2.33 from the total because females make 2.33 dollars less than males.

Q6 Interpret the Intercept.

Hint: Provide a technical interpretation.

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.

options(scipen=999)
data(CPS85, package="mosaicData")
wage_lm <- lm(wage ~ educ + exper + sex + union,
                data = CPS85)

# View summary of model 1
summary(wage_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        0.00000010459 ***
## educ         0.93495    0.07835  11.934 < 0.0000000000000002 ***
## exper        0.10692    0.01674   6.387        0.00000000037 ***
## sexM         2.14765    0.39097   5.493        0.00000006145 ***
## 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: < 0.00000000000000022

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.