Data has been collected on 30 randomly selected towns: hide data Number of motor vehicle Population No. of recorded Average temperature accidents per year (x 1000) traffic offences (x 100) PF 1,004 266 152 84 741 58 164 84 597 170 77 78 836 416 49 81 1,414 499 165 78 1,000 372 120 79 888 490 45 80 343 6 71 76 785 17 185 78 1,083 461 97 82 762 273 97 78 813 360 76 85 722 488 3 78 920 109 192 80 864 431 57 83 687 312 56 83 790 332 59 82 822 418 55 77 1,506 495 195 81 445 35 85 82 536 65 98 81 1,143 389 152 77 486 225 41 85 1,098 324 145 75 225 18 47 81 912 451 71 76 691 317 62 82 428 194 32 77 1,212 287 191 79 989 126 189 76You are part of a team investigating the identifying motor vehicle accidents. A multiple regression model is to be constructed to predict the number of motor vehicle accidents in a town per year based upon the population of the town, the number of recorded traffic offenses per year and the average annual temperature in the town. Data has been collected on 30 randomly selected towns: show data a) Find the multiple regression equation using all three explanatory variables. Assume that X, is population, X2 is number of recorded traffic offenses per year and X3 is average annual temperature. Give your answers to 3 decimal places. y = population + no. traffic offences + average temp b) At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis rejected. For parts c) and d), using the data, separately calculate the correlations between the response variable and each of the three explanatory variables. c) The explanatory variable that is most correlated with number of motor vehicle accidents per year is: population number of traffic offenses average annual temperature d) The explanatory variable that is least correlated with number of motor vehicle accidents per year is: population number of traffic offenses average annual temperature e) The value of R2 for this model, to 2 decimal places, is equal to f) The value of se for this model, to 3 decimal places, is equal to g) Construct a new multiple regression model by removing the variable average annual temperature. Give your answers to 3 decimal places. The new regression model equation is: y = 1 +L population + no. traffic offences h) In the new model compared to the previous one, the value of RZ (to 2 decimal places) is: O increased O decreased O unchanged i) In the new model compared to the previous one, the value of se (to 3 decimal places) is: O increased O decreased unchanged