You collect the monthly income and the number of lottery ticket purchased per month from 500 individuals. You find this data in problem 1 on “Homework 5 data". a. [2

Points] You wish to estimate the relationship: \text { Income }_{i}=\beta_{0}+\beta_{1} \text { Lottery }_{i}+\mu_{i} Why might this regression yield to bias estimates of B1? b. [2 Points] Plot Income; and Lottery; and describe it. Does the relationship look linear? C. [1 Points] Estimate the regression \text { Income }_{i}=\beta_{0}+\beta_{1} \text { Lottery }_{i}+\mu_{i}(1) in excel. Report the values of R^2, adj-R^2, Mean Square Error (Standard Error of the Regression), AIC,and BIC. d. [2 Points] Plot In (Income;) and Lottery; and describe it. Does the relationship look linear?Which relationship better aligns to the 1st assumption of OLS? [1 Points] Estimate the regressionе. \ln \left(\text { Income }_{i}\right)=\alpha_{0}+\alpha_{1} \text { Lottery }_{i}+\epsilon_{i}(2) in excel. Report the values of R², adj-R?, Mean Square Error (Standard Error of the Regression), AIC,and BIC. Interpret, in words, the value of â. f. [10 Points] Why can't you compare the values of the Mean Square Error, AIC, and BIC of models(1) and (2)? How does the transformation of Income; affect these statistics? g. [10 Points] Some derp comes to you and argues that model (1) is better because it has a higher R2 and adj-R2. Is derp correct? Why or why not?