questions 1, 2, 3, 4, 5, and 6

Use the following to answer questions 1-9: A random sample of 79 companies from the Forbes 500 list (which actually consists of nearly 800 companies) was selected and the relationship between sales (in hundreds of thousands of dollars) and profits (in hundreds of thousands of dollars) was investigated by regression. Using the simple linear regression model (profits), = + (sales), + 0 where the deviations fare assumed to be independent and Normally distributed with mean O and standard deviation . The following results were obtained from statistical software: R' - 0.662 - 466.2 Variable Parameter estimate Standard error Constant -176.644 61.16 Sales 0.092498 0.0075 1. What is (approximately) the value of the intercept of the least squares regression line? A)0.0075 61.16 B) 0.0925 D) -176.64 2. What is an (approximate) 90% confidence interval for the slope ? A)-0,09 4 0.0075 0.09 = 0,0075 B) 0,09 + 0.0125 DI 0,09 =0,0125 3. Suppose the researchers conducting the study wish to test the hypotheses H,: 7 -0 versus H: 7 2 0. What do we know about the P-value of this test? A) The P-value is greater than 0.10. B) The P-value is between 0. 05 and 0, 10. C) The P-value is between 0.01 and 0.05. D) The P-value is less than 0.01. 4. Is there strong evidence of a straight-line relationship between sales and profits" Explain briefly A) Yes, because the slope of the least squares line is positive. B) Yes, because the P-value for testing if the slope is O is quite small. C) No, because the value of the square of the correlation is relatively small. Dy It is impossible to say, because we are not given the actual value of the correlation. Use the following additional information to answer questions 5 and 6: Suppose the researchers conducting this study wish to estimate the profits (in hundreds of thousands of dollars) for companies that had sales (in hundreds of thousands of dollars) of 500. The following results were obtained from statistical software: Sales Predicted profit Standard error 95.0% C.I. 95.0% P.I. -130.4 59.3 (-248.5. -12.3) (-1066.4, 805.6) 5. If the researchers wish to estimate the mean profits for all companies that had sales of 300. what would be a 95% confidence interval for the mean profits? A)(-1066.4. 805.6) C) -130 4 +59.3 B) (-248.5. -12.3) D) 500 # 59.3 6. If the researchers wish to estimate the profits for a particular company that had sales of 500, what would be a 95% prediction interval for the profits? A)(-1066.4. 805.6) C) -130.4 + 59.3 B) (-248.5, -12.3) D) 500 + 59_3