Read this scenario and answer the questions a,b,c,d,e,f,g,h A policy analyst for a state legislative services agency has been assigned the task of determining why average length of sentence to be served in state prisons by Class B felons varies by county in the state. In order to identify these important causal factors, the analyst decides to use multiple regression analysis. She obtains previous studies and background material dealing with the factors that are important determinants of sentence length. Both the local crime rate and the median length of time local judges have served on the bench have been consistently identified in previous research and theory as critical causal factors. Both of these variables have been found to be positively related to average sentence length. Beyond this information, the analyst can identify no other factors that have been consistently related to the dependent variable. However, various other factors appear to be important in some of the states for which relevant studies are available. The analyst hypothesizes that both median years of schooling and population density will have a significant influence upon average sentence length. Furthermore, she feels that the education variable will be negatively related to average sentence length and that population density will be positively related to average sentence length. The analyst sets up the following regression model for the analysis: ASLi = [31+ (32 CR; 'l' [33 MBTi 'l' [34 MYSi 'l' [35 PDi 'l' Ui where: ASLi = average sentence length for Class B felons from county i (measured in months), CR: = crime rate for county i (measured in number of serious crimes per thousand population), MBT. = median bench time ofjudges in county i (measured as years on the bench), MYSi = median years of schooling per capita in county i, and PD: = population density of county i (measured as average number of people per square mile). The analyst collects the necessary data for all 72 counties of the state for the previous year and runs an OLS regression. The results she obtains from the computer output are: ASLi = 8.53 + 0.87 CR; + 2.75 MBT. - 0.47 MYSr + 0.042 PD; + What sen; = 0.06 sens = 1.54 sew = 0.12 5835 = 0.0032 F = 253.11 R2 = .920 adj. R2 = .906 n = 72 VlFs: CR = 2.96 MBT = 11.54 MYS = 4.17 PD = 13.07 Standardized Betas: CR = .645 MBT= .338 MYS = .478 PD = .177 Part 2 Part 2 a. State the null hypothesis concerning the statistical significance of the overall regression, test this hypothesis, and interpret the results. (Use a .01 level of significance} (3 points) b. Test the statistical significance of the individual partial regression coefficient estimators of [32 and [35, first stating the respective hypotheses. Interpret the results. (Use a .01 level of significance.) (3 points} c. Interpret the values of the estimators of the partial regression coefficients (33 and B4. (3 points) d. i) How do you know that near multicollinearity is present in the regression? ii} Which variables are involved, and what is the potential impact of this near multicollinearity on the relevant estimators and their tstatistics? (3 points} 6. Which is the most important independent variable in explaining average sentence length? How do you know? [2 points] f. Interpret the value of the adjusted R2 for this problem. Why is it a better statistic to use than the unadjusted R2? [2 points] g. Write a paragraph that interprets the overall results for the director of the legislative services agency. (3 points] h. In 1983, Hardline County is expected to have the following characteristics: CR = 13, MBT = 8.8, MYS = 7.4, and PD = 518. What would be the projected value of ASL for this county? If these values are outside the range of values used for the regression, would this be a reliable forecast? Why or Why not? (3 points)