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 ~ sex + exper + educ,
                data = CPS85)

# View summary of model 1
summary(wages_lm)
## 
## Call:
## lm(formula = wage ~ sex + exper + educ, 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 ***
## sexM         2.33763    0.38806   6.024      0.0000000031877 ***
## exper        0.11330    0.01671   6.781      0.0000000000319 ***
## educ         0.94051    0.07886  11.926 < 0.0000000000000002 ***
## ---
## 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 eduaction is statsiticaly signifacant because at when you look at the p value is it is less then 5%, you can tell by the number of 0’s before the 2 showing its less than 5%.

Q3 Interpret the coefficient of education.

Hint: Discuss both its sign and magnitude.

The actaul coefficnet of education would be 94 cents. Every additional year of education that person obtains, they recieve an extra 94 cents hourly.

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.

Based on the graph there is evidence to suggest there is gender discrimination with wages. The coeifficent is postive with male gender being statisticaly and the magnitued iis over two.

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

A prediction for womens wages would be 8.15 dollars hourly if they had 15 years education and 5 years expirence. This number is obtained by multiplying the two coefcients by the reflecting year and subtracting the the intercept.

Q6 Interpret the Intercept.

Hint: Provide a technical interpretation.

when the predictors are all at zero, the intrcept becomes the the value of the wage, wich would be -6.50451.

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 ~ sex + exper + educ + union,
                data = CPS85)

# View summary of model 1
summary(wages_lm)
## 
## Call:
## lm(formula = wage ~ sex + exper + educ + 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 ***
## sexM         2.14765    0.39097   5.493        0.00000006145 ***
## exper        0.10692    0.01674   6.387        0.00000000037 ***
## educ         0.93495    0.07835  11.934 < 0.0000000000000002 ***
## 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.