12. For an ice cream stand near a public beach, the number of daily ice cream sales has been recorded during a two-week

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12 For An Ice Cream Stand Near A Public Beach The Number Of Daily Ice Cream Sales Has Been Recorded During A Two Week 1 (82.16 KiB) Viewed 28 times

12. For an ice cream stand near a public beach, the number of daily ice cream sales has been recorded during a two-week period in June, along with the average temperatures of each day. The data from the sample is shown below: 78 75 81 82 82 97 94 96 84 79 average temperature (°F) 65 74 76 number of ice cream sales 95 103 113 118 125 134 136 121 105 128 124 131 127 120 (a) (2 points) Compute the values of n, ny, 12 y, and r.y. You may use a calculator or a spreadsheet to calculate these values. (b) (3 points) Use the values in the previous part to calcuate Sex, Syy and Scy, and show the formulas you used. (c) (5 points) Use the values found in (a) and (b) to determine the least squares esti- mates for the slope 31, intercept Bo and variance of the linear regression model Y = Be + Berate, where € (0,0%) are independent. Show all formulas you used. You may express your answers the nearest thousandths place. Page 11 (d) (10 points) Perform a model utility test on the linear regression model, i.e., test the null hypothesis that B1 = 0 versus the alternative hypothesis that B. 70 using Student's t distribution, at a significance level a = 0.05. Be sure the list the test statistic, the value of the test statistic, the rejection region and the conclusion of the hypothesis test. (e) (5 points) Determine r, the sample correlation coefficient. You may express your answer to the nearest thousandths place. Based on this value of r, how strong is the correlation between the two random variables?