Stat 401 A XM Homework 11On-Campus Due Date: Wednesday, December 3Off-Campus Due Date: Wednesday, December 101. An exercise physiologist wanted to compare the body-fat-reducing effects of three exercise programs(A, B, and C) and varying levels of a dietary supplement (0, 1, 1.5, and 2 g/day). A total of 24 malesbetween 28 and 35 years of age were used for the study. The males were assigned in a completelyrandomized manner to the 12 combinations of exercise program and dietary supplement level. Aftercompleting 12 months of training according to the assigned exercise program and consuming the dietarysupplement at the assigned rate, the body fat of each male was measured. The body fat of each male alsohad been measured prior to the start of the treatment regimes. The variable bfchange in the SAS codeaccompanying this assignment gives the body fat before treatment minus body fat after treatment foreach subject. Use the code and output to answer the following questions. Please assume that the multipleregression model fits the data well and that all the assumptions of multiple regression are satisfied.(a) Estimate the mean change in body fat for each exercise program when no dietary supplement isconsumed. Also provide a 95% confidence interval for the exercise-program-C/no-supplementmean in addition to the estimated mean.(b) Is there a statistically significant difference between the estimated means for exercise programs Aand C computed in problem 1? Provide an appropriate test statistic, p-value, and conclusion.(c) By how much does the mean change in body fat for exercise-program-C subjects taking 2 g/day ofthe supplement differ from the mean change in body fat for excercise-program-C subjects taking 1g/day of the supplement? Provide a 95% confidence interval for the difference in means.data one;input exprog $ dietsupp bfchange;cards;A 0.0 0.6A 0.0 0.3A 1.0 1.4A 1.0 1.9A 1.5 1.8A 1.5 2.3A 2.0 2.5A 2.0 2.7B 0.0 0.6B 0.0 0.4B 1.0 0.7B 1.0 1.2B 1.5 1.3B 1.5 1.5B 2.0 1.6B 2.0 1.8C 0.0 0.7C 0.0 0.1C 1.0 0.51C 1.0 0.6C 1.5 0.8C 1.5 0.9C 2.0 0.9C 2.0 1.0;data one; set one;x1=dietsupp;if exprog=’A’ then x2=1;else x2=0;if exprog=’B’ then x3=1;else x3=0;x4=x1*x2;x5=x1*x3;run;proc reg;model bfchange=x1 x2 x3 x4 x5;run;Dependent Variable: bfchangeSum of MeanSource DF Squares Square F Value Pr > FModel 5 10.96687 2.19337 50.44 <.0001Error 18 0.78271 0.04348Corrected Total 23 11.74958Root MSE 0.20853 R-Square 0.9334Dependent Mean 1.17083 Adj R-Sq 0.9149Coeff Var 17.81026Parameter EstimatesParameter StandardVariable DF Estimate Error t Value Pr > |t|Intercept 1 0.36286 0.13422 2.70 0.0145x1 1 0.28857 0.09970 2.89 0.0097x2 1 0.12571 0.18981 0.66 0.5162x3 1 0.09000 0.18981 0.47 0.6411x4 1 0.77714 0.14099 5.51 <.0001x5 1 0.32000 0.14099 2.27 0.035822. An experiment was conducted to examine the ability of four drugs (A, B, C, and D) to delay atrophy indenervated muscles. A certain leg muscle in each of 48 rats was deprived of its nerve supply by surgicallysevering the appropriate nerves. The rats were divided into four groups of 12 rats each. Each drug wasassigned to one of the groups. After 14 days, the 12 rats from each group were killed. The weight of thedenervated muscle (in grams) was obtained from each of the sacrificed rats.The denervated muscles should undergo atrophy and begin to shrink in size. A treatment effectivelydelays atrophy if it seems to prevent or reduce muscle shrinkage during the 14-day period. The bestway to measure atrophy would be to take the weight of the muscle before treatment minus the weight ofthe muscle after treatment. Unfortunately the weight of the muscle before treatment cannot be obtainedwithout killing the rat. Consequently the initial total body weight (in grams) of each sacrificed rat wasmeasured. It is assumed that this figure is closely related to the initial weight of the muscle. Ultimatelywe will want to look for differences in mean after-treatment muscle weight among the drugs, whilecontrolling/adjusting for differences in initial weight. The data is contained in the file denervated.sas.(a) One way to analyze the data would be to assume that the muscle weights before treatment wereabout the same for each rat. Then the only relevant data are the after-treatment muscle weights forthe 12 rats in each treatment group. A high mean after-treatment muscle weight will suggest thata treatment is effective. Drugs A, B, and C are experimental drugs. Drug D is a control – simplya saline solution that could not affect atrophy. Assuming that the muscle weights before treatmentwere about the same for each rat, are any of the experimental drugs more effective than the control?If so, which ones? Provide appropriate statistical evidence to support your answer.(b) If the before-treatment muscle weights were not the same for each rat, the analysis in part 1 wouldbe inefficient at best and perhaps flawed. Examining the initial body weights of the rats suggeststhat there was probably quite a bit of variation in before-treatment muscle weights. This needs to beaccounted for in analysis. One way to account for differences in before-treatment muscle weightswould be to conduct a multiple regression analysis. The response variable would be after-treatmentmuscle weight. The explanatory variables would include initial body weight and indicator variablesfor the drug (i.e., treatment) factor. It would then be possible to make comparisons among the drugswhile adjusting for the effect of body weight. For example, we could make a statement like“Among rats with the same initial body weight, the mean after-treatment muscle weightfor rats treated with drug A was estimated to begrams larger than the mean after-treatment muscle weight for rats treated with the control (95% confidence interval tograms larger).”Conduct such an analysis for this data set. When adjusting for differences in body weight, are anyof the experimental drugs more effective than the control? If so, which ones? Provide appropriatestatistical evidence to support your answer.(c) The analysis in part (b) assumes that there is no interaction between the drug factor and initial bodyweight. In other words, the analysis assumes that the differences in the mean after-treatment muscleweights among the four drug treatments are the same for any initial body weight. Is that assumptionappropriate? Provide appropriate statistical evidence to support your answer.(d) The 48 rats were kept in a large cage prior to treatment. The