HHS 526: Linear Regression in Public Health Final Project Total points: 30 Instructions. This final project is a strictly individual effort; do not consult with anyone about this exam, but you may use any other sources (e.g., books, notes, internet). Answer all parts to the problem. Show all work so that partial credit can be earned. Include all R code that you use and the relevant output from it with your answers. Please upload your solutions to Canvas by Wednesday of Finals Week no later than 11:59pm PST. (30 points) A randomized trial was conducted to assess how two coping styles are associated with handling physical discomfort in children. 300 children aged 8-11 years were enrolled in the study. The response variable was the duration (in seconds) that each child could keep their right arm submerged in cold water; this was the method use to induce discomfort. The response variable is named duration in the data file.

At the beginning of the study, each child met with a psychologist who asked questions that were designed to determine the child's natural coping style. Based on the answers to those questions, each child was classified as having either an attender coping style or a distractor coping style. As the name implies, distractors try to distract themselves from what is happening (e.g., think about playing outside with their friends). Attenders take a "mind over matter" approach to handling physical discomfort in that they concentrate on what is happening and try to overcome their discomfort. This variable is named copingattend (1=attender, 0=distractor) in the data file.

Each child was randomized to receive training to be better at using the attender coping mechanism or the distractor coping mechanism. This variable is named distractortraining (1=child received distractor training, 0=child received attender training) in the data file.

The other candidate predictor variables are age in months (agemonths), sex (male; 1=male, 0=female), and socioeconomic status of the household (ses).

a. (10 points) Use the all possible regressions procedure to select a model. Do not consider interactions. Use adjusted R2 as the selection criterion. Write the selected model.

b. (10 points) Use the backward elimination approach to select a model. Do not consider interactions. Use alpha level of 0.05. Write the selected model.

c. (10 points) Use the forward selection approach to select a model. Do not consider interactions. Use alpha level of 0.05. Write the selected model. Note that different approaches can lead to different models.

Data:

duration copingattend distractortraining male agemonths ses 30.0 1 0 1 107 58 31.8 1 1 0 113 54 26.8 0 0 1 121 56 49.8 0 1 1 119 79 46.5 0 1 0 128 48 27.2 0 0 1 110 46 36.9 1 1 0 124 79 43.2 0 0 0 103 59 33.6 0 0 0 111 72 50.2 0 0 1 113 73 55.0 0 1 0 119 73 53.6 1 1 1 112 54 61.0 0 1 1 127 61 44.3 0 1 0 110 59 26.4 1 0 0 128 64 55.1 0 1 1 124 56 12.2 1 0 1 121 46 27.4 1 1 0 120 61 48.8 0 1 1 128 51 33.0 0 0 1 115 55 47.7 0 1 1 127 79 39.6 1 1 0 102 75 55.5 0 1 1 115 71 60.6 0 1 0 103 46 27.9 0 0 1 127 78 49.0 0 1 1 116 66 24.5 0 0 0 126 74 57.3 0 1 1 105 63 34.1 0 0 1 103 52 40.0 1 0 1 106 52 47.1 0 1 0 127 57 44.9 1 0 1 119 74 54.0 0 1 1 101 82 34.9 1 1 1 109 58 35.5 1 0 1 122 54 26.8 1 0 1 118 81 64.3 0 1 1 109 61 56.8 0 1 1 114 62 46.1 1 1 1 119 78 52.7 0 1 1 105 68 36.8 0 0 0 109 84 20.1 0 0 0 109 50 20.2 1 0 0 126 60 53.3 1 1 0 112 79 19.8 0 0 0 101 52 35.4 1 1 1 103 82 20.2 0 0 0 118 60 34.0 0 0 1 117 75 64.4 0 1 1 120 84 23.3 0 0 0 102 77 32.1 0 0 0 121 49 55.3 0 1 1 105 77 43.7 1 1 0 126 64 50.3 0 1 1 117 72 51.5 0 1 1 111 50 34.4 0 0 0 108 70 47.8 0 1 1 116 53 32.7 0 0 1 127 61 27.3 1 1 0 113 63 42.0 1 0 1 115 59 48.6 1 1 0 116 61 38.9 1 1 0 116 82 44.4 0 0 1 112 78 37.3 0 0 1 113 65 22.6 1 0 1 108 46 25.8 0 0 1 114 52 29.1 0 0 1 108 70 44.7 0 1 1 116 59 54.0 0 1 1 110 75 39.0 0 0 0 125 77 16.4 1 0 1 101 79 34.1 0 0 0 116 46 35.7 0 1 1 125 77 30.4 1 0 1 120 61 29.3 1 0 1 125 59 28.6 0 0 1 125 68 39.1 0 0 1 116 61 70.8 0 1 1 128 83 30.5 0 0 0 113 72 41.7 1 1 1 108 67 45.6 1 1 1 119 73 39.6 1 1 0 109 57 48.4 1 1 1 104 64 54.8 0 1 0 123 84 56.4 0 1 1 119 78 39.6 1 1 0 119 65 36.0 0 0 0 117 75 50.7 0 1 1 121 69 41.6 1 1 1 112 73 59.6 0 1 1 107 53 55.6 0 1 1 114 47 44.1 0 1 1 127 55 37.3 0 0 1 102 67 32.3 0 0 1 107 63 44.1 0 1 0 116 67 16.3 0 0 1 105 82 44.9 1 1 1 121 54 33.6 0 0 0 124 51 33.6 0 0 0 112 71 16.0 1 0 0 106 60 47.7 0 1 0 110 56 46.0 0 0 1 111 73 19.4 1 0 0 123 69 33.8 1 1 1 120 80 46.0 1 1 1 116 57 44.0 0 0 1 104 83 29.2 1 1 0 126 52 39.9 1 1 0 106 60 26.7 1 0 1 128 54 23.8 1 0 1 107 70 51.9 0 1 1 109 66 64.1 0 1 1 117 84 33.5 0 0 0 114 80 33.9 0 0 1 124 73 17.2 1 0 1 123 51 39.0 1 1 1 105 71 53.1 1 1 1 125 58 40.0 0 0 1 108 58 65.5 0 1 1 108 74 38.4 1 1 1 112 59 42.8 0 1 0 114 62 26.0 0 0 0 114 61 27.7 1 1 0 120 51 43.3 0 1 1 102 75 63.3 0 1 1 128 82 74.4 0 1 1 128 78 28.8 0 0 0 127 78 27.9 1 0 1 122 52 25.9 0 0 0 118 57 11.8 1 0 1 123 72 10.1 1 0 0 120 77 33.1 0 0 1 110 79 40.3 1 1 1 106 55 37.5 0 0 1 102 77 34.1 1 1 1 107 68 47.3 0 1 1 108 47 31.6 0 0 1 119 84 55.6 0 1 0 121 51 27.7 1 0 1 107 61 46.5 0 1 0 128 50 39.3 0 1 0 115 83 41.8 1 1 1 107 64 45.3 0 1 0 116 80 53.3 0 1 0 121 47 55.7 0 1 0 103 72 47.5 0 1 0 103 69 43.4 1 1 0 105 47 17.6 1 0 0 112 63 34.4 1 1 0 116 79 56.1 0 1 1 103 51 36.3 0 0 1 114 62 29.2 1 0 0 115 77 62.8 0 1 1 105 50 47.1 0 1 0 123 46 31.5 0 0 0 111 82 49.0 0 1 1 127 46 28.2 1 1 0 113 68 22.0 1 0 1 125 82 37.8 0 0 0 110 57 44.7 1 1 1 123 47 32.3 0 0 1 106 49 30.7 0 0 0 112 52 39.6 1 1 0 110 47 60.9 0 1 1 106 57 33.7 0 0 1 104 73 52.5 0 1 1 114 73 20.8 1 0 0 127 63 50.2 1 1 1 101 50 54.3 0 1 1 125 56 18.8 1 0 1 103 76 24.8 0 0 0 114 63 14.1 1 0 1 117 84 41.9 1 1 1 112 47 57.6 0 1 1 106 60 51.4 0 1 1 115 52 35.9 0 0 1 124 60 52.9 1 1 1 111 70 44.1 0 0 1 104 66 45.3 1 1 1 108 74 25.4 1 0 1 127 76 37.9 0 0 1 117 82 56.0 0 1 0 124 82 54.1 0 1 0 122 66 49.1 1 1 1 122 49 49.5 0 1 0 108 77 15.0 1 0 1 121 58 52.2 0 1 0 124 66 33.9 0 0 1 111 55 32.9 1 0 1 105 51 42.2 1 1 0 112 50 45.2 0 0 1 117 65 45.3 1 1 0 119 56 20.5 0 0 1 117 79 24.0 0 0 1 108 64 32.5 0 0 1 121 74 30.9 0 0 1 110 83 18.7 1 1 0 112 76 24.4 0 0 1 119 78 12.3 1 0 0 111 58 50.9 0 1 0 124 46 38.0 1 0 1 102 50 62.8 0 1 1 108 74 38.3 0 0 1 111 57 27.0 1 1 0 127 67 50.9 1 1 0 126 75 40.0 0 0 1 118 61 64.0 0 1 1 109 70 26.4 1 0 1 109 48 41.2 1 1 1 108 51 23.1 0 0 0 118 51 35.2 1 1 0 124 68 48.2 1 1 1 124 69 25.3 0 0 0 125 77 23.7 1 0 1 121 79 14.7 1 0 0 128 74 31.6 1 0 1 117 83 17.1 1 0 1 105 52 48.2 1 1 1 127 60 31.6 0 0 1 122 72 50.4 0 0 1 127 61 51.7 1 1 1 104 64 44.7 0 0 0 126 82 58.5 0 1 1 102 73 34.1 0 0 1 120 74 24.1 0 0 0 118 55 49.3 1 1 1 114 49 15.5 1 0 0 116 74 49.3 1 1 1 104 59 56.7 0 1 1 118 48 41.0 0 0 1 115 51 57.6 0 1 1 120 77 55.9 1 1 1 112 60 48.8 0 0 1 104 51 50.8 0 0 1 127 47 37.1 0 0 1 102 69 31.0 0 0 0 123 54 31.8 0 1 0 114 80 48.8 0 1 0 113 67 35.2 1 1 1 108 60 35.0 1 1 1 115 72 21.3 1 0 0 104 50 27.2 1 0 1 117 70 46.2 0 0 1 120 84 48.1 0 1 0 122 60 55.1 1 1 1 119 74 22.5 1 0 1 114 50 23.6 1 1 0 116 52 40.5 0 0 1 102 66 34.6 0 0 1 126 79 40.2 0 0 1 107 73 49.6 0 1 1 119 57 33.1 0 0 0 109 78 46.3 0 1 1 117 84 16.6 1 0 0 109 61 50.0 0 1 1 101 74 64.5 0 1 1 112 65 50.1 0 1 0 123 78 34.3 0 0 0 109 54 31.9 0 0 1 115 72 57.8 0 1 0 106 84 36.8 0 0 0 105 62 45.4 0 1 0 116 51 23.6 0 0 0 122 78 30.1 0 0 0 101 79 66.7 0 1 1 125 60 25.7 1 0 1 118 68 52.5 0 1 0 112 69 22.7 1 0 1 121 64 16.3 1 0 0 116 79 42.0 0 1 0 126 51 40.6 0 0 1 102 67 51.7 0 1 1 106 54 38.4 1 1 0 104 70 31.8 0 0 1 127 62 55.6 0 1 1 127 56 23.9 1 0 0 127 76 36.8 0 0 1 124 78 58.2 0 1 1 120 53 41.4 1 1 1 103 63 51.2 1 1 0 117 55 41.2 1 1 0 101 76 30.4 0 0 1 126 50 39.5 0 0 1 106 67 40.4 1 1 0 106 51 41.1 1 1 0 114 76 53.1 0 1 0 116 53 15.8 1 0 0 104 84 47.1 0 1 0 109 60 31.9 1 1 1 106 52 26.3 0 0 0 103 57 28.7 1 1 1 120 74 53.5 0 1 1 118 81 48.3 0 1 1 126 80 35.9 1 1 0 103 46 39.4 0 1 1 116 76 33.6 0 0 1 124 64 35.9 0 1 1 117 79 35.8 0 0 1 123 48 50.5 1 1 1 114 48 36.7 0 0 1 118 80