STAT 331 Homework 2 1. Multiple Choice: In testing the hypotheses H0: B1 = 0 vs. Ha: B1 0 with alpha = 0.05, the calculated value of our test statistic is T = 3.45. The critical value from our t-table is t0.025 = 2.306. What conclusion should be made? a) Do not reject H0, there is evidence that X contributes information to the prediction of Y. b) Reject H0, there is evidence that X contributes information to the prediction of Y. c) Do not reject H0, there is not evidence that X contributes information to the prediction of Y. d) Reject H0, there is not evidence that X contributes information to the prediction of Y. 2. Given the sum of square values: SSxy = -29.5, SSxx = 17.5, and SSyy = 51.51. Calculate SSE. (Hint: do not round your calculations until the very end) (round your final answer to two decimal places) 3. The table below gives data for a statistical experiment. (This is the same data used in question number 6 on HW 1). The least squares prediction equation for this data is ^y = 3 + 1.2x. Find the values of s2 and s. (round your final answers to three decimal places) X -2 -1 0 1 2 Y 1 1 3 5 5 4. The following information was calculated for a least squares regression analysis: n = 20, SSxy = 204, SSxx = 100, SSyy = 516, 1-hat = 2.04, 0-hat = 3.12, and SSE = 99.84. Preform a hypothesis test to see if X contributes information to Y using alpha = 0.05. a) What is the value of your test statistic? (Round your final answer to three decimal places) b) What critical value from the t-table will be used in the rejection region? 5. Multiple Choice: Which of the following is the correct interpretation of the coefficient of determination r2 = 0.78? a) b) c) d) There is a strong negative linear relationship between X and Y. 22% of the variation in the Y-values is being explained by the model. 78% of the variation in the Y-values is explained by having X in the model. There is a weak linear relationship between X and Y. 6. Using the following information: n = 7, SSxx = 15, SSxy = 30, SSyy = 80, SSE = 20, B1-hat = 2, s2 = 4. a) Create a 95% confidence interval for B1. (Round your final answers to three decimal places.) b) Find the value of the coefficient of determination. (Round your answer to two decimal places.) 7. Multiple Choice: What is the correct interpretation of the coefficient of correlation r = 0.94? a) b) c) d) There is a strong negative linear relationship between X and Y. 94% of the variation in the Y-values is explained by the model. There is a weak positive linear relationship between X and Y. There is a strong positive linear relationship between X and Y