15. A survey of students at California Polytechnic State University collected data to investigate the effect of backpack weight on whether or not students had back problems. Potential predictors include Ratio (the ratio of backpack weight to body weight), Year in school, Units (number of credits currently taking), and iMale (an indicator of being male); we'll call this full model Model 1. Output for this study is located in the appendix. log (9( I} 1 l9( )) 2 30 + lRatio + giMale + g'ngllltS + 5'34Year (Backpack Model 1) .l' (a) (7 points) Consider whether an interaction between Year and Ratio should be added to the model; use the output to carefully explain to a layman why or why not this interaction should be added. (b) (10 points] Is it possible to remove variables Year and Units from Model 1? Model 2 uses only the predictors Ratio and iMale. Conduct a hypothesis test and make an appropriate conclusion about which model should be used. Be sure to state your hypotheses, calculate your test statistic, and make a conclusion in context; you may assume relevant assumptions are met. log (L!) 1 a J) : 3'30 + 381Ratio + _.i-9gil\\-'Iale (Backpack Model 2) i I? (c) (7 points) One study suggests that a person should not carry more weight in a backpack than 10% of body weight (corresponding to a Ratio value of 0.1). Use Model 2 (regardless of your answer above) to calculate probabilities of back problems for men and women at that backpack weight. (d) (6 points) For a backpack weight that is 10% of body weight (Ratio 2 0.10). calculate the odds ratio of back problems for men as compared to women. Report and interpret the 95% condence interval. Show your work. Use Model 2 again. Backpack Problem 0 0 4oo dato 060 0 O A Year A-0- -- 0 0 0 00 OfA O Back Probe? O No 4- Yes O - 0.05 0.10 0.15 Ratio Backpack Model 1: log 1 -8(x) = Bo + Bi Ratio + BiMale + By Units + 3, Year Coefficients: Estimate Std. Error z value Pr(>|21) (Intercept) -2.26402 1.93701 -1.169 0. 2425 Ratio 9. 35392 6. 28989 1. 487 0. 1370 SexMale -1. 18145 0. 48834 -2.419 0. 0155 * Units 0. 07834 0. 12005 0.653 0. 5141 Year 0. 02732 0. 16980 0. 161 0. 8722 Null deviance: 125.37 on 99 degrees of freedom Residual deviance: 114.48 on 95 degrees of freedom AIC: 124.48e(I) Backpack Model 2: log 1 - 0(x) = Bo + BiRatio + BziMale Coefficienta: Estimate Std. Error z value Pr(>Izl) (Intercept) -1.0495 0. 5759 -1.822 0.0684 Ratio 9.7786 6.2046 1.576 0. 1150 SexHale -1.2329 0. 4810 -2.563 0. 0104 + Null deviance: 125.37 on 99 degrees of freedom Residual deviance: 114.93 on 97 degrees of freedom AIC: 120.93 > pchisq (114. 48,95, lover . tail-F) [1] 0. 08466299 > pchisq (114. 93,97, lover. tail=F) [1] 0. 1033376 > pchisq (0.45, 2, lower. tail-F) [1] 0.7985162