library(tidverse) library

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 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%?

It is statistically significant because the P value of education is less than 5%

Q3 Interpret the coefficient of education.

Hint: Discuss both its sign and magnitude. For every unit of education which is defined in years there is an additional 94 cents added to the 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.

There is infact evidence for gender discrimiation in wages because the coifficent sign is postive. Males are statistically significant the magnitude of the coeficcent is over 2

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

The predicted wage of a women with 15 years of education and 5 years experience would be 8.15 dollars per hour. To recieve this number one must multiply the two coefiicents by the years then subtract the intercept.

Q6 Interpret the Intercept.

Hint: Provide a technical interpretation. If all the predictors are at 0 then the intercept is the value the wage will become, in which this number is -6.50451 dollars per hour

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 1.05e-07 ***
## sexM         2.14765    0.39097   5.493 6.14e-08 ***
## exper        0.10692    0.01674   6.387 3.70e-10 ***
## educ         0.93495    0.07835  11.934  < 2e-16 ***
## 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

The second model is better because the residual standard error is lower then the first becasue it is 4.42 compared to 4.45 This means that the real wage and the wage predicted by the model are closer then the actual wage. ```

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.