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")
cps85_lm <- lm(wage ~ educ + exper + sex,
                data = CPS85)

summary(cps85_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, education is statistically significant at 5% becuase its P value is smaller than .05.

Q3 Interpret the coefficient of education.

Hint: Discuss both its sign and magnitude.

Every 1 year that you continue your education you gain .94051 dollars for every hour of work.

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.

Yes, because it seems that males are making 2.33763 more dollars an hour than women. This is statistically significant because it sits with 3 *** meaning it is very statistically significant because its lower then .05.

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

The hourly wage for a woman with 15 years of education and 5 years of experience would be $8.15 an hour. How to: (.94 times 15)+(.11 times 5)+-6.5

Q6 Interpret the Intercept.

Hint: Provide a technical interpretation.

The intercept at 0 would be statistically impossible. People would be making a negative profit.

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")
cps85_lm <- lm(wage ~ educ + exper + sex + union,
                data = CPS85)

summary(cps85_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 adjusted R code went from 2.489 to 2.592 after adding union to the model. Also, in the first model without the union variable, the residual standard error is 4.454 and on the model included union is 4.423. The second model is better due to more accuracy and information of union memebers.

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.