3. {13 pts] Using data from the American Community Survey, you want to predict person's income person's income from hours worked per week, race (white, black, Asian, other], and gender {male, female]. You hope to build a reasonable and useful regression model by entering and removing predictors- in a stepwise mannerinto your model. 3.1 {3 pts] You have predictors which are good candidates for being the first to enter the stepwise model. How would you determine the first predictor? Use the regression summary output [from simple regression model with each variable} below to answer the following questions [3.2 8: 3.3}: Estimate Std. Error tvalue Pr [:- ltl ] {Intercept} 2?82.5?26 66?6.5534 0.42 0.66211 hrs_work 124?.2128 146.2013 8.53 0.0009 race:black J35653090 63.93.2168 1.50 0.135 race: Asian 3513166156 86903484 4.12 0.0002 race:other 11112.8611'I T213322!) 1.54 0.1238 gender:fernale 464300916 3303.4?00 4.32 0.0000 " " " You can't add or drop individual levels of a variable when a variable was dummy coded. 3.2 {3 pts] What's the reference group? 3.3 {4 pts] Which variable [if any] should be added from the model first when doing forwards selection using the p-value approach? Justify your answer. 3.4 {3 pts] You built the model based on the regression output. What criteria would you consider building a good model from the results of any stepwise regression procedure? In addition, state at least two reasons that you should be careful in the stepwise regression procedure