Answer Happy

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: average temperature (°F) number of ice cream sales 65 74 78 75 95 103 113 118 76 81 82 125 134 136 82 97 94 86 84 82 79 121 105 128 124 131 127 120 (a) (2 points) Compute the values of n, Pxi. Pyi, Px 2 i, Py2i, and PXiyi . You may use a calculator or a spreadsheet to calculate these values. (b) (3 points) Use the values in the previous part to calcuate Sxx, Syy and Sxy, and show the formulas you used. (c) (5 points) Use the values found in (a) and (b) to determine the least squares estimates for the slope B1, intercept BO and variance o 2 of the linear regression model Yi = BO+B1xi + ei, where ei ~ N(0,02) are independent. Show all formulas you used. You may express your answers to 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 B1=0 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. CCCC (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?