# 0 observed values for area are also below the

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0, observed values for Area are also below the regression line, so this prediction is probably an overestimate. 4. The residual plot for Model I: Log (Area) vs. Time shows a random scatter of points on either side of the line residuals = 0, suggesting a good fit. 5. Model I: log Area 0.34057 0.115582 Time , so for 5.5 seconds, 0.97627 2 log Area 0.34057 0.115582 5.5 log Area 0.97627 Area 10 9.47 cm .
598 The Practice of Statistics, 4/e- Chapter 12 © 2011 BFW Publishers Test 12A Part I 1. d ―SE Coef‖ stands for standard error of the coefficient— slope in this case. This is the estimate (from the sample) of standard deviation of the sample distribution of slope. 2. e S = 145.851 is the standard deviation of the residuals, and thus measures how far, on average, observed word counts are from word counts predicted by the regression equation. 3. a The P - value for this test is on the line ―File size‖ and is therefore 0.022. A P -value less than the level of significance provides enough evidence against H 0 to reject it. 4. d Statement I is not a condition required for regression inference. The Normality condition requires that the value of the response variable be Normally distributed at each value of the explanatory variable. Statements II a nd III are the ―Equal variance‖ and ―Linear‖ conditions. 5. b 0.092498 is the slope of the sample regression line, and thus estimates the change in the predicted value of the response variable for a one-unit change in the explanatory variable. 6. c Margin of error is ( critical value)*(standard error of estimate). The critical t for 90% confidence and 40 2 = 38 degrees of freedom is not in table B, but must be slightly larger than the critical t for 40 degrees of freedom, which is 1.684, thus the correct choice must be 1.686 0.0106 . 7. d Statement I is the appropriate interpretation of a ―U - shaped‖ pattern in residuals. Statement II is true because the residuals near x = 1982 are all below the regression line, so the line overestimates observed values. Without the scatterplot, we cannot determine whether number of employees increases or decreases with year, so we don’t know if Statement III is correct. 8. b If , then log log log x y ab y a b x , so the relationship between log y and x is linear with slope log b and intercept log a . 9. b The ―Coef‖ column provides the slope and intercept of the regression equation for the transformed variables. This regression is for log y vs. so the equation is log 449.7 0.228 y x . 10. c ln 5.36 3.216 ln12 5.36 3.216 2.4849 2.632 W , so 2.632 13.894 W e Part II 11. (a) L inear: the scatterplot shows a weak linear relationship between sleep and GPA, and the residual plot shows a random scatter of points about the line residual = 0. I ndependent: Study time and score for randomly-selected students should be independent. We are sampling without replacement, but there are more than 10 10 100 students in the class. N ormal : The Normal probability plot of the residuals is roughly linear, which suggests that test scores are roughly Normally distributed for each value study time. E qual variance: the small sample size makes