Need it in R-code. Thank you? 7. Consider the uswages data in the Faraway packag

Question

Need it in R-code. Thank you?

7. Consider the uswages data in the Faraway package. (20 Points) (a) Create a new predictor called region which takes values "NE", "MW","WE", and "SO", and summarizes the variables ne, mw, we, and so in the data set (b) Turn region into a factor variable with "NE" as the baseline. Fit the regression model with region as the predictor and wage as the outcome. Summarize the fit of the model and use an F-test to determine if region is significantly associated with wages (take a - 0.05). Take special care to interpret what each of the betas represents (c) Now use "SO" as the baseline and redo (b). Contrast the results. (d) Keep "SO" as the baseline. Now use an F-test to determine if region is still significant after correcting for education. Use ?-0.1 (e) Keep "SO" as the baseline. Now fit a model with eduction, region, and their interaction. Summarize of the fit of the model (paying attention to how to inter- pret the betas) and use an F-test to determine if the interaction effect is, overall, significant. (f) Plot the results from (e) by creating a scatter plot of wage vs education. Color code the points by region and plot the regression lines for each region (make sure the color of the regression line matches the color of the points)

Explanation / Answer

The R snippet is as follows

library(faraway)

data("uswages")
uswages

attach(uswages)
## ne as baseline
uswages$region = ifelse(so==1, "so",ifelse(mw==1,"mw",ifelse(we==1,"we","ne")))

uswages$region <- as.factor(uswages$region)

fit <- lm(wage ~ region,data=uswages)
summary(fit)

## so as baseline

uswages$region1 = ifelse(ne==1, "ne",ifelse(mw==1,"mw",ifelse(we==1,"we","so")))

uswages$region1 <- as.factor(uswages$region1)

fit1 <- lm(wage ~ region1,data=uswages)
summary(fit1)

The results are

summary(fit)

Call:

lm(formula = wage ~ region, data = uswages)

Residuals:

Min 1Q Median   3Q Max

-596.1 -295.9 -86.8 176.4 7135.2

Coefficients:

Estimate Std. Error tvalue Pr(>|t|)   

(Intercept) 585.368 20.600 28.416 <2e-16 ***

regionne 46.291   29.746 1.556 0.1198   

regionso -4.532   27.601 -0.164 0.8696   

regionwe 64.598   30.439 2.122 0.0339 *  ## signficant as the p value is less than0.05

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘’ 1

Residual standard error: 459.2 on 1996 degrees of freedom

Multiple R-squared: 0.00405, Adjusted R-squared: 0.002553

F-statistic: 2.705 on 3 and 1996 DF, p-value:0.04395 ## F test , overall the model is statisticallysignficant

> summary(fit1)

Call:

lm(formula = wage ~ region1, data = uswages)

Residuals:

Min 1Q Median   3Q Max

-596.1 -295.9 -86.8 176.4 7135.2

Coefficients:

Estimate Std. Error tvalue Pr(>|t|)   

(Intercept) 585.368 20.600 28.416 <2e-16 ***

region1ne 46.291   29.746 1.556 0.1198   

region1so -4.532   27.601 -0.164 0.8696   

region1we 64.598   30.439 2.122 0.0339 * ##signficant as the p value is less than 0.05

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘’ 1

Residual standard error: 459.2 on 1996 degrees of freedom

Multiple R-squared: 0.00405, Adjusted R-squared: 0.002553

F-statistic: 2.705 on 3 and 1996 DF, p-value:0.04395 , as the p value of the model is less than 0.05 , hence themodel is overall significant

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