Question 2 Suppose that you have just started your rst job as a junior data analyst for the Niagara Regional Police and your supervisor has asked you to describe the relationship between temperature and crime. You have the data on the average temperature and the corresponding numbers of crimes reported on the following ve days in June: Temperature {Celsius} " 12:37 Table 1: Average temperature and reported crime in June (a) Use the 0L3 formulas provided in class to regress the number of crimes (if?) on the corresponding temperature {Xi-j. That is, estimate the following regression model: 1rl=3n'l'4'31X:"l"\"r Ell Report your estimates 30 and '5']; Show your work. (h) Use the formula provided in class to estimate the sampling variance of the regession coeicient for 1. That is! nd c'rl. (c) Use your estimates to test the following hypothesis: Hail-31:\" Hill-31:?\" Based on your result, which conclusions you can [or cannot) draw about the relationship between temperature and crime? (d) Your supervisor gives you the weather forecast for tomorrow, which indicates it will be 19 degrees celsius. How much crime does the model suggest there will be? That is._ calculate K. (e) After taking your results up the chain of command. your supervisor is back to ask you whether your estimated relationship will work during the winter [where temperatures will be below I} celsius). 1What do you say? # 7148010 Day # N. . 7 42 : 21 14 + 37 - and in data a Ov: 25 xi = 419 y = 23.8 3221 5 * = 645.8 A.= 13.8 - ( 0.12657 = 145. 8) 80 = = 48, 9539 if the eshmates ac ,= a.nzest and Q B = 2 Xly - 5xy J. * -48.1539 BI = 0.172657 by ji - Bo . B, xi 1= 16 95095 43 3 21.8061 "2 . 30.96119 5, : 19. 76484 Chag 1 30.80726 * Standard error .45.+ - (B. ) - 5-2 4 x 328 2307 12,966 . 8 OB,= 0.091857 i. the sampling vanance of the regression Coefficient for B, *= 16 OBI = 0.091857 H. : B, =0 the list stahshe. 0. 112459 0.041857