library(tidyverse)
library(scales)
options(scipen = 999)

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      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%?

The coefficent of education is statistically signifigant at 5% because 0.0000000000000002 is much lower than 5. You can see it in the data set of CPS85 that the pvalue of eductation is less than 5%.

Q3 Interpret the coefficient of education.

Hint: Discuss both its sign and magnitude.

The coefficient education displays that for every additonal year of educaton you recieve you earn 94 more cents an hour to your wage.

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.

If you take a closer look you can see that there is gender discrimination in wages. In the chart you can easily see that men are paid more than women by a good amount. The men have a $2.01 greater wage than the females wages.

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

If you do some calculations the prediction of a womens wage who has 15 years of education and 5 years of work experience would be $8.15/hr.

Q6 Interpret the Intercept.

Hint: Provide a technical interpretation.

When all predictions are at the value 0 the intercept is showing the value of the wages paid.

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        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

The second model is much better than the first one we created. If you look at the standard error, it is lower on th second model than the first and R Squared is higher in the second model than in the first.

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.