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She asks her research assistant to conduct a study to

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Unformatted text preview: 95% confident that the mathematics test score is estimated to be at least 61.69 and at most 68.55. This is based on the assumption that 50% of the teachers have a mathematics degree, the average age is 43 and the average salary is $48,300. t.025,32 = 2.036 Distance value = (1.68/7.6209)2 = 0.0486 65.12 ± 2.036 (7.6209) = 61.69 to 68.54 AACSB: Analytic Bloom's: Application Difficulty: Hard Learning Objective: 6 Topic: Confidence & prediction intervals 1-1445 Chapter 01 - An Introduction to Business Statistics 122. A member of the state legislature has expressed concern about the differences in the mathematics test scores of high school freshmen across the state. She asks her research assistant to conduct a study to investigate what factors could account for the differences. The research assistant looked at a random sample of school districts across the state and used the factors of percentage of mathematics teachers in each district with a degree in mathematics, the average age of mathematics teachers and the average salary of mathematics teachers s = 7.62090 Analysis of Variance Additional information related to this point estimate of 65.12 is given below. Predicted Values for New Observations 50% with math degree, average age of 43 and average salary is 48.3 New Calculate the 95% prediction interval for this point estimate. 49.22 to 81.02 t.025,32 = 2.036 Distance value = (1.68/7.6209)2 = 0.0486 65.12 ± 2.036 (7.6209) = 49.22 to 81.02 AACSB: Analytic Bloom's: Application Difficulty: Hard Learning Objective: 6 Topic: Confidence & prediction intervals Chapter 15 1-1446 Chapter 01 - An Introduction to Business Statistics Model Building and Model Diagnostics True / False Questions 1. If we increase the number of independent variables in a multiple regression model, the F statistic will always increase. True False 2. When the quadratic regression model y = shows the rate of curvature of the parabola. True False 0 + x+ 1 x2 + ε is used the term 2 1 3. The variance inflation factor measures the relationship between the dependent variable and the rest of the independent variables in the regression model. True False 4. Even when an unimportant variable is added to a regression model, the explained variation will increase. True False 5. The standard error decreases if and only if the adjusted multiple coefficient of determination decreases. True False 6. One way to identify outliers with respect to their x values is to calculate their leverage values. True False 1-1447 Chapter 01 - An Introduction to Business Statistics 7. Cook's distance is a way to determine whether an observation is influential. True False 8. An independent variable dropped during an iteration of the backward elimination process may be added back to the regression model during a later iteration of the process. True False 9. In comparing regression models, the regression model with the largest R2 will also have the smallest standard error(s). True False 10. Multicollinearity hinders the regression model's ability to predict the dependent variable on the basis of a combination of values of the independent variable in the experimental region. True False 11. In a multiple regression mode if the largest VIF is 21.6, then it can be concluded that there are indications of multicollinearity. True False 12. In multiple regression analysis, if the simple correlation coefficient between the dependent variable and one of the independent variables is .95, then this indicates that the problem of multicollinearity exists. True False 13. When there are indications of autocorrelation, first an investigation should be conducted to determine whether one or more independent variables that might explain the autocorrelation have been omitted from the model. True False 1-1448 Chapter 01 - An Introduction to Business Statistics 14. If a particular multiple regression model has a small value of the C statistic and C for this model is less than k + 1, where k is the number of independent variables in the model, then the model should be considered biased and therefore undesirable. True False Multiple Choice Questions 15. The general form of the quadratic multiple regression models is: A. y = 1X1 + 2X2 + B. y = 0 + 1X1 + 2X2 + C. y = 0 + X+ D. y = 0 + E. y = 0 + 1 X2 + 1 1 2 X2 + X1 + X22 + 2 16. As we increase the number of independent variables in a multiple regression model, the F statistic will _____ increase. A. Always B. Sometimes C. Never 17. In the quadratic regression model zero, then the parabola opens __________. A. Less than, upward B. Greater than, upward C. Greater than, either upward or downward D. Less than, either upward or downward E. Equal to, downward if the term 1-1449 2 is ______ Chapter 01 - An Introduction to Business Statistics 18. In the quadratic regression model the: A. Rate of curvature of the parabola. B. Value of Y when X is zero. C. Shift parameter of the parabola. D. Y-intercept of the parabola. the 19. In the quadratic regression model the: A. Rate of curvature of the parabola. B. Value of Y when X is zero. C. Shift parameter of the parabola. D. Y-intercept of the parabola. , the v2 term represents 2...
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