4. Using the data-set described in question 3. The following model is considered: Death Rate, Bo+ B₁Doctor_A; + B₂Hospital_A; + B3A_Income; + B4Pop_Den, + (2 = for i = 1,..., 53, where ; represents the error in the model. The estimated coeffi cients and their standard errors are: coef Estimate Std. Error Во 12.26 2.02 B₁ 0.007 0.006 B2 0.0005 0.0007 B3 -0.33 0.23 B4 -0.009 0.004 (a) Interpret the estimated coefficients? I [6] (b) Test and interpret the hypothesis Ho 3 = 0 against H₁: B3 0 using a t-test. Given that to.025,48 = 2.01. [4] (c) Test and interpret the following hypotheses, Ho: B3 B4 = 0 using an F-test. Given that F0.05,2,48 3.19 and the ANOVA table below: Df Sum Sq Doctor A 1 1.926 Hospital A 1 0.918 A_Income 1 8.195 Pop_Den 1 9.614 Residuals 48 123.074 [6] (d) How would I modify the model in (2) to include the categorical variable State. The possible States in this data set are: Ohio, Indiana, Illinois, Iowa, Missouri, Nebraska, Kansas, and Oklahoma. [2] (e) Calculate and interpret the adjusted coefficient of multiple determination R²? [2] (f) Provide an interpretation of each of the diagnostic plots in Figure (2) for the regression model in (2) (i.e. provide a short description of what the plot can be used to assess and an interpretation for the particular plots provided). [10] 1.5 Standard widual 5:0 1.0 0.0 Re ° Residuals vs Fitted Figure 2: Diagnostic plots for the regression model in (2) 04 T T T T T 7.5 8.0 8.5 9.0 9.5 10.0 10.5 Fed values Scale Location 31 Standardized residuals -2 1- Standardized residuals -1 - Normal Q-Q 03 T T -2 -1 0 1 2 Theoretical Quartles Residuals vs Leverage 7.5 8.0 8.5 9.0 9.5 10.0 10.5 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Fed values Leverage Cook's distance Mo