Question

Information from 20 houses was used to develop a regression model to predict the cost of air conditioning, y, in SR, using the variables x1- daily minimum outside temperature in °F x2-thickness of insulation in inches Predictor Constant Coef SE Coef 90.78 1.23 10.06 448.3 2.7 4.93 2.23 1.58 15.9 S 40.91 Analysis of Variance Source DF MS Regression Residual Error Total 28452.60 39395.62 Use the above information to answer the following four questions 23) The percentage of variation explained by the model is a) b) c) d) 10.94% 27.78790 39.39% 40.91% 24) A 95% confidence interval for the expected change in heating costs as a result of a change in the daily minimum outside temperature is a) Between SR0.1520 and SR5.3721 b) Between SR5.2919 and SR37.174 c) Between SR204.78 and SR497.17 d) Between SR4.3860 and SR36.380

Answer 1

23)% of variation explained by model =R² =1-SSE/SST=1-28452.6/39395.62=0.2777 ~ 27.77%

24) here for 95% CI and (n-3=17) degree of freedom ; critical value of t =2.110

therefore 95% CI for slope =estimate -/+ t*std error =-2.7 -/+ 2.110*1.23 =0.11 ; 5.30