library(tidyverse)
library(scales)

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(wage ~ educ + exper + sex,
                data = CPS85)

# View summary of model 1
summary(wages)
## 
## 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 significant at 5%

Q3 Interpret the coefficient of education.

Hint: Discuss both its sign and magnitude.

There are three stars after the data meaning that there is a 99.9% chance that the coefficiant is true. Meaning 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 that there is gender discrimination in determining wages because when looking at sex, the significance is 99.9% making the coefficiant true. The sign is positive meaning that there is evidence that there is gender discrimination in wages, and the magnitude of 2.33 means that males will make 2.33 times more then the avg wage

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 edjucation and 5 years of experience is $14.67

Q6 Interpret the Intercept.

Hint: Provide a technical interpretation.

The intercept is -6.50451 which means that the wage would be $6.5 if all other variables were 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(wage ~ educ + exper + sex + union,
                data = CPS85)

# View summary of model 1
summary(wages)
## 
## 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

In the new model the risidual error is 4.423 compared to the first model of 4.454. The second model is better becuase the 4.423 is closer to the actual wage price.

In the new model the reported adjusted r squared is 0.2592 and in the older model it was 0.2489. This means that there is a 26% of wage can be shown in the model, and in the first model only 25% can be shown in the model making the second model better.

The second model is 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.