Please answer Q7

you can use R studio, and put the data into txt file.

the Pulse.txt dataset:

Active Rest Smoke Gender Exercise Hgt Wgt 97 78 0 1 1 63 119 82 68 1 0 3 70 225 88 62 0 0 3 72 175 106 74 0 0 3 72 170 78 63 0 1 3 67 125 109 65 0 0 3 74 188 66 43 0 1 3 67 140 68 65 0 0 3 70 200 100 63 0 0 1 70 165 70 59 0 1 2 65 115 98 57 0 0 3 72 175 140 65 0 1 3 66 135 105 85 0 1 1 64 140 84 64 0 0 3 75 207 134 70 0 1 2 68 150 117 66 0 1 2 65 120 100 72 0 0 3 74 200 108 72 0 0 3 67 170 76 75 0 0 2 70 155 86 68 1 0 2 73 195 110 72 0 1 3 66 130 65 61 0 1 3 66 145 85 74 0 1 1 68 135 80 72 0 0 1 70 135 87 72 1 0 2 70 173 133 97 0 1 1 65 130 125 64 0 1 3 70 172 61 53 0 0 3 70 175 117 78 0 0 2 74 160 90 85 0 1 2 65 120 110 80 0 1 1 68 145 68 58 0 0 3 74 175 102 77 1 0 2 72 200 67 53 0 0 3 68 158 112 75 0 1 2 64 125 86 51 0 0 3 74 195 85 74 0 1 3 64 120 66 59 0 0 3 69 175 73 47 0 1 3 62 145 85 72 0 0 1 72 140 110 78 0 0 1 69 165 97 72 0 1 1 64 135 93 70 0 1 1 67 115 86 63 0 1 3 65 145 80 60 0 1 3 60 106 96 80 0 1 2 67 140 74 67 0 0 3 68 150 124 64 0 0 2 73 260 78 65 0 0 1 72 150 93 72 0 0 2 71 160 80 65 0 0 2 75 245 80 67 1 1 2 65 133 92 69 0 0 3 68 210 69 60 0 0 3 72 205 82 62 0 0 3 74 194 88 67 0 1 1 64 135 74 71 0 0 1 70 190 74 62 0 0 2 71 200 75 54 0 0 3 72 149 120 66 0 1 2 67 150 105 77 0 1 3 67 138 104 82 0 1 2 65 120 99 78 1 0 3 71 165 113 64 0 0 2 70 160 67 58 0 1 3 68 135 125 80 1 1 3 65 125 133 92 1 0 1 69 185 98 67 0 1 2 64 140 80 64 0 1 3 71 135 91 65 1 0 2 67 150 76 63 0 1 3 63 135 78 52 0 0 3 75 215 94 74 0 1 2 64 160 150 64 0 0 2 71 170 92 66 0 0 3 77 180 96 67 1 1 2 64 165 68 58 0 1 3 67 140 82 62 0 1 3 62 145 102 77 0 1 1 63 124 69 63 0 0 2 69 140 65 69 0 0 3 71 165 84 64 0 0 3 72 185 86 60 1 1 1 68 150 84 61 0 1 2 65 115 116 70 1 1 2 70 150 88 71 0 1 1 61 110 65 63 0 1 3 64 120 101 75 0 0 1 64 110 89 71 0 1 3 61 150 128 64 0 1 3 67 133 68 56 0 1 3 66 160 90 72 0 0 2 67 130 80 65 0 0 3 69 150 80 63 0 0 1 70 135 98 79 0 0 2 74 180 90 61 0 0 3 71 183 82 68 0 1 1 64 120 97 61 0 1 3 64 113 90 67 1 0 2 74 180 98 67 0 1 2 63 150 88 54 0 0 3 67 176 94 69 0 0 2 72 195 92 58 1 0 2 65 165 96 76 0 1 2 67 155 80 68 0 1 2 64 135 66 55 0 1 3 65 125 110 83 1 1 1 63 114 87 80 0 1 2 69 141 88 56 0 1 3 68 172 94 83 0 0 1 66 110 96 74 0 1 2 67 123 89 78 0 0 3 67 145 74 61 0 0 3 75 180 111 75 0 0 2 71 180 81 72 0 1 3 70 135 98 63 1 0 3 78 238 99 78 0 1 2 63 115 65 54 0 0 3 74 190 95 80 0 0 3 72 175 127 69 0 1 2 64 135 76 50 0 0 3 71 208 102 69 0 1 2 63 110 88 67 0 0 2 68 157 125 80 0 1 1 61 110 72 63 1 0 2 72 210 76 68 0 1 2 62 137 112 64 0 0 3 70 192 69 48 0 1 3 67 140 101 82 0 1 3 64 125 72 64 0 1 3 63 145 112 79 1 1 1 69 130 81 61 0 0 3 68 160 90 73 0 1 2 67 140 96 75 0 1 1 66 135 66 59 0 0 2 70 175 114 74 0 1 2 67 150 71 66 0 1 2 62 102 75 60 0 0 2 70 160 102 76 0 0 3 70 160 138 92 0 1 1 64 120 85 71 0 1 3 68 130 80 72 0 0 3 70 180 107 68 0 0 2 67 155 119 81 0 1 2 61 130 98 68 0 0 3 72 195 95 58 0 0 2 74 225 95 63 0 1 2 69 125 76 84 0 0 1 71 155 96 74 0 1 2 63 116 102 78 0 0 2 71 154 82 68 0 0 3 72 195 99 66 0 1 2 65 145 80 70 0 0 2 70 175 83 72 0 0 2 73 175 102 84 0 1 2 64 150 102 77 0 0 2 72 187 106 78 0 1 2 66 154 79 63 0 1 3 68 140 80 60 0 1 3 61 115 79 68 1 0 2 69 163 110 80 0 1 2 61 125 144 106 0 1 1 62 140 80 73 0 0 2 70 155 97 73 0 1 1 67 115 60 55 0 0 3 72 160 80 62 0 0 3 72 193 108 63 0 0 3 71 165 107 75 0 1 2 67 150 51 54 0 0 3 74 150 68 72 0 0 1 70 205 80 63 0 0 3 71 183 80 74 0 1 2 68 139 60 58 0 0 3 70 168 64 60 0 0 3 71 165 87 70 0 0 2 73 210 110 95 1 0 1 69 180 110 88 0 1 2 66 145 82 70 1 0 1 70 185 154 82 0 0 1 71 250 139 72 1 1 1 63 112 86 58 0 0 3 70 185 95 68 0 1 3 64 145 112 90 0 1 2 61 122 120 81 0 0 2 71 150 79 69 0 0 3 71 148 64 48 0 0 3 69 170 84 60 0 0 2 72 177 65 75 1 1 2 65 145 60 54 0 0 3 73 194 79 58 0 1 3 67 150 79 53 0 0 2 72 172 70 55 0 1 3 68 150 75 71 0 0 2 70 175 107 65 0 1 2 65 128 78 68 1 0 2 72 165 74 62 0 0 2 73 180 80 68 0 0 3 69 160 121 94 1 0 1 74 250 120 58 0 0 3 71 187 96 74 0 1 2 70 151 75 73 0 0 1 71 152 106 78 0 1 2 61 122 88 63 0 1 2 69 145 91 58 0 1 2 68 143 98 70 0 0 3 70 245 63 53 0 1 3 65 107 95 63 0 0 2 73 192 85 67 0 1 2 70 165 83 55 0 0 3 70 190 92 68 0 1 3 67 135 81 64 0 1 1 66 145 89 60 0 1 2 62 136 103 73 1 0 1 71 220 110 74 0 1 2 66 130 78 66 0 0 2 70 185 122 80 0 0 3 67 150 122 98 0 1 1 62 105 71 57 0 1 3 65 145 65 61 0 0 3 71 175 92 70 0 0 1 76 260 93 71 0 1 2 67 175 88 57 0 0 3 76 230 90 73 0 0 3 70 205 56 52 0 1 3 66 145 95 70 0 1 2 66 150 83 64 0 0 3 68 135 97 55 0 0 3 67 175 105 85 0 1 2 64 150 82 74 0 1 3 66 124 102 81 0 0 2 69 172 87 67 0 0 2 68 170 81 62 0 0 3 68 151

k. Fit the model from part j. Write out the estimated regression equation. 1. What is the 32 value and 6'5 of this interaction model, and how do those values compare to the model that was t in part e. ? 7. We will use the Pulse.txt dataset for this question. This dataset is from an observational study where subjects had their resting pulse rate (beats per minute), height (in inches), weight iii (in pounds), smoking status (1 for smoker and 0 for non-smoker), and active pulse rate (beats per minute) recorded. We will use resting pulse rate as the response variable Y, and explanatory variables of weight as X1 and smoking status as X2. Run the following line in R after you have imported the data set to create a new variable called "Smoker" with categories Yes and No. pulse$Smoker ifelse (pulse$3moke==1 , "Yes " , "No ") a. Fit a model in R using response variable Y and only the covariate X2 of smoking status. Test if the coefficient on X2 is equal to 0. State the null and alternative hypothesis, the test statistic, p-value and make a conclusion. b. Now conduct a two sample t-test with equal va.raince in R, where the response is resting pulse rate and the two groups fsamples are smokers and non-smokers. How does this test correspond to the test from part a. ? c. Write out the population model where we have response Y and covariates f explanatory variables X1 and X 2 with no interaction term in context of the study. d. With respect to the effect of weight on resting pulse rate, what does it mean in context of the study that we do not have an interaction term (with smoking status) in the model from part c. '? Explain in a sentence or two. e. Fit the model from part c. in R and report the coefcient of determination (multiple R2 value) and report the estimate of 05. f. How many observations are there in the dataset? g. Using the model output from part e., test the coefficient on Smoking yes (X2) being equal to U or not. Write the null and alternative hypothesis, test statistic, pvalue, and make a conclusion in context of the study (be careful of your wording). h. Can we conclude that smoking causes lower resting pulse rates? Why or why not? i. Create a scatterplot where X=Weight and Y=Resting pulse rate, and have different colors and symbols for the different smoking groups. Interpret this scatterplot. j. Now add an interaction term between smoker yes and weight to your model from part c., and write out the population model