4. (14 points) The city of London often experiences dense fog. Data was collected for a severe 15-day period including the number of deaths per day (Y) and mean atmospheric smoke (X in mg/m3). The regression output from Minitab is given below with some output missing. Coefficients Term Coof SE Coef T-Value P-Value VIF Caneast 171.8 31.4 547 0300 Smoke 153 Model Summary S Raq R-ac(adj) R-sqlpred] 81.7036 57.15% 43.71% Analysis of Variance Source DF Adj 55 AdjMS F-Value P.Value 1.15450 17.14 Snolie 1 136450 17.34 Error 102102 7EGG Lack of FIL 11118 Pure Error EESO 2672 14 236752 a) (2 points) Give the equation of the regression line. b) (10 points) Conduct a hypothesis test to see is there is a significant positive linear relationship between mean atmospheric smoke and number of deaths. Assume any necessary conditions to be true. Take a = 0.05 c) (2 points) Find the value of the residual if 135 deaths were recorded on a day with mean atmospheric smoke of 0.49. 5. (14 points) A random sample of smokers was obtained, and each individual was classified both with respect to gender and with respect to the age at which he/she first started smoking. The data from the study is summarized below: Pie Chart of Age Gender Male Female Below 16 years 25 10 Age 16 - 17 years 24 32 18-20 years 28 17 Above 20 years 19 34 a) (4 points) The graph above shows the conditional distribution of Age using Gender as a conditioning variable. Do you think Gender and Age are associated based on the plot? b) (10 points) Conduct a hypothesis test to see if Gender and Age are associated. Do you get to the same conclusion as in part a)? Take a = 0.05