CASE 1 UPDATED

# CASE 1 UPDATED - [Simple LR Exercise For 70 randomly...

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[Simple LR Exercise] Time For 70 randomly selected 1999 National League baseball games, here are the times given 108 to complete the games (in minutes), the total number of hits in the game, and the combined 128 number of runs in the game. 129 136 Time Hits Run Time Hits Run 137 108 10 5 170 19 11 141 128 11 8 170 19 13 143 129 12 1 171 16 9 143 136 18 16 172 9 4 146 137 13 6 172 18 7 146 141 14 5 176 20 9 146 143 15 3 176 20 10 149 143 12 6 177 20 7 150 146 13 6 178 17 6 151 146 19 5 178 17 13 152 146 16 10 179 17 10 152 149 16 6 180 19 14 152 150 21 13 181 16 9 153 151 13 6 181 25 13 154 152 20 14 181 16 10 157 152 14 3 183 17 11 157 152 18 4 187 20 11 158 153 8 3 188 14 6 158 154 15 6 189 19 11 159 157 20 6 320 23 9 159 157 12 6 320 22 12 160 158 19 11 325 21 11 160 158 19 13 329 24 14 161 159 25 15 336 23 12 161 159 21 10 342 26 22 164 160 14 3 342 23 14 166 160 9 3 342 20 6 167 161 13 6 350 16 9 169 161 18 12 375 21 11 169 164 19 13 378 27 19 169 166 23 12 385 27 19 170 167 16 13 387 30 22 170 169 14 6 400 32 37 171 169 19 9 440 24 13 172 169 16 7 453 20 9 172 176 a. Find a regression equation for the following: 176 a.1 Time (independent var) vs hits (dependent var) 177 a.2 Time (independent var) vs runs (dependent var) 178 b. Are all assumptions of simple LR met in the two regression analysis made? If not, which 178 one(s) is/are violated? Why did you say so? Show plots. If any violation is detected make the 179 appropriate remedy. 180 c. Prove the significance of both models obtained above. Which dependent variable can time 181 predict better- hits or runs? Justify your answer using statistical quantities or indices. 181 d. Look at your residual plot (especially residual vs predicted or residual vs independent var plots)? 181 What do you observe? How do you remedy the problem you are seeing (clue: evaluate the behav 183 of the data through scatter plots.) 187 e. Re-run the analysis according to the remedy you plan to do in d. What conclusion could you give 188

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189 320 320 325 329 336 342 342 342 350 375 378 385 387 400 440 453
Hits Run 10 5 11 8 12 1 18 16 13 6 14 5 15 3 12 6 13 6 19 5 16 10 16 6 21 13 13 6 20 14 14 3 18 4 8 3 15 6 20 6 12 6 19 11 19 13 25 15 21 10 14 3 9 3 13 6 18 12 19 13 23 12 16 13 14 6 19 9 16 7 19 11 19 13 16 9 9 4 18 7 20 9 20 10 20 7 17 6 17 13 17 10 19 14 16 9 25 13 16 10 17 11 20 11 14 6 108 158 208 258 0 5 10 15 20 25 30 35 Time v Ti Hits 25 30 35 40 Time v

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19 11 23 9 22 12 21 11 24 14 23 12 26 22 23 14 20 6 16 9 21 11 27 19 27 19 30 22 32 37 24 13 20 9 108 158 208 258 0 5 10 15 20 Runs
Time Hits 128 11 129 12 136 18 137 13 141 14 143 15 143 12 146 13 146 19 146 16 149 16 150 21 151 13 152 20 152 14 152 18 153 8 154 15 157 20 157 12 158 19 158 19 159 25 159 21 160 14 160 9 161 13 161 18 164 19 166 23 167 16 169 14 169 19 169 16 170 19 170 19 171 16 172 9 172 18 176 20 176 20 177 20 178 17 178 17 179 17 180 19 181 16 181 25 181 16 183 17 187 20 188 14 189 19 308 358 408 Hits ime Runs

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53 cases 308 358 408 Time
Run Time 8 108 1 128 16 129 6 136 5 137 3 141 6 143 6 143 5 146 10 146 6 146 13 149 6 150 14 151 3 152 4 152 3 152 6 153 6 154 6 157 11 157 13 158 15 158 10 159 3 159 3 160 6 160 12 161 13 161 12 164 13 166 6 167 9 169 7 169 11 169 13 170 9 170 4 171 7 172 9 172 10 176 7 176 6 177 13 178 10 178 14 179 9 180 13 181 10 181 11 181 11 183 6 187 11 188 128 138 148 158 168 178 188 0 5 10 15 20 25 30 f(x) = 0.0857185591x + 2.7658841234 Hits (53 cases) 128 138 148 158 168 178 188 0 2 4 6 8 10 12 14 16 18 Runs (53 cases)

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189
Hits Run 10 5 11 8 12 1 18 16 13 6 14 5 15 3 12 6 13 6 19 5 16 10 16 6 21 13 13 6 20 14 14 3 18 4 8 3 15 6 20 6 12 6 19 11 19 13 25 15 21 10 14 3 9 3 13 6 18 12 19 13 23 12 16 13 14 6 19 9 16 7 19 11 19 13 16 9 9 4 18 7 20 9 20 10 20 7 17 6 17 13 17 10 19 14 16 9 25 13 16 10 17 11 20 11 14 6 108 118 128 138 148 158 168 178 188 0 5 10 15 20 25 30 Hits 108 118 128 138 148 158 168 178 188 0 2 4 6 8 10 12 14 16 18 Run (54 cases)

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19 11
Time Hits Run 108 10 5 128 11 8 129 12 1 136 18 16 137 13 6 141 14 5 143 15 3 143 12 6 146 13 6 146 19 5 146 16 10 149 16 6 150 21 13 151 13 6 152 20 14 152 14 3

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