x 8 12 14 17 23 30 40 46 55 67 72 83 96 112 127 y 4 10 13 14 15 25 27 47 38 46 53 74 82 99 101 Use the general software output to decide whether there is a useful linear relationship between rainfall and runoff Predictor Intercept Coef 1 752 Stdev 2 530 t 0 69 p value 0 5008 rainfall 0 841 0 039 21 59 0 0000 S 5 566 R sq 97 38 R sq (adj) 97 1 State the least squares regression equation State the appropriate null and alternative hypotheses OHO B 0 H B 0 Ho 10 H 1 Ho P1 0 Ha 0 Ho B 0 H P 0 From the output state the test statistic value and find the P value (Round your test statistic to two decimal places and your P value to four decimal places ) t P value State the conclusion in the problem context (Use 0 05 ) Reject Ho There is a useful linear relationship between runoff and rainfall at the 0 05 level Reject Ho There is not a useful linear relationship between runoff and rainfall at the 0 05 level Fail to reject Ho There is not a useful linear relationship between runoff and rainfall at the 0 05 level Fail to reject Ho There is a useful linear relationship between runoff and rainfall at the 0 05 level

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x 8 12 14 17 23 30 40 46 55 67 72 83 96 112 127 y 4 10 13 14 15 25 27 47 38 46 53 74 82 99 101 Use the general software output to decide whether there is a useful linear relationship between rainfall and runoff  Predictor Intercept Coef  1 752 Stdev 2 530 t  0 69 p value 0 5008 rainfall 0 841 0 039 21 59 0 0000 S   5 566 R sq 97 38 R sq (adj)   97 1  State the least squares regression equation    State the appropriate null and alternative hypotheses  OHO  B   0 H B  0 Ho  10 H 1 Ho  P1   0 Ha   0 Ho B   0 H P   0 From the output state the test statistic value and find the P value  (Round your test statistic to two decimal places and your P value to four decimal places ) t  P value  State the conclusion in the problem context  (Use   0 05 ) Reject Ho  There is a useful linear relationship between runoff and rainfall at the 0 05 level  Reject Ho  There is not a useful linear relationship between runoff and rainfall at the 0 05 level  Fail to reject Ho  There is not a useful linear relationship between runoff and rainfall at the 0 05 level  Fail to reject Ho  There is a useful linear relationship between runoff and rainfall at the 0 05 level

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x 8 12 14 17 23 30 40 46 55 67 72 83 96 112 127 y 4 10 13 14 15 25 27

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