MATH 534 Week 6 Homework Problems

1. Question: Which of the following is not an assumption of the regression model? 2. Question: Suppose for a given data set the regression equation is: y = 54.78 + 1.45x, and the point (0.00, 24.78) is in the data set. The residual for this point is _________. 3. Question: If the standard error of the estimate for a regression model fitted to a large number of paired observations is 1.75, approximately 68% of the residuals would lie within________. 4. Question: For a regression model y = 30 − 2x, the coefficient of determination was determined as equal to 0.81. The coefficient of correlation is ________. 5. Question: To test if the slope coefficient β1 in the population regression model is significantly different from zero, a hypothesis test is conducted on the slope coefficient b1 in the regression equation developed using sample data. This test is a _____________. 6. Question: The proportion of variability of the dependent variable accounted for or explained by the independent variable is called the ____________. 7. Question: In the regression equation, y = 2.164 + 1.3657x, n = 6, the mean of x is 8.667, SSxx= 89.333 and Se = 3.44. A 95% prediction interval for y when x = 8 is _____________. 8. Question: A manager wishes to predict the annual cost (y) of an automobile based on the number of miles (x) driven. The following model was developed: y = 2,000 + 0.42x. If a car is driven 15,000 miles, the predicted cost is ___________-. 9. Question: A manager wishes to predict the annual cost (y) of an automobile based on the number of miles (x) driven. The following model was developed: y = 2,000 + 0.42x. If a car is driven 20,000 miles, the predicted cost is ___________. 10. Question: A hospital administrator developed a regression line, y = 30 + 2x, to predict y = the number of full-time employees (FTE) needed using x = the number of beds. The slope of this regression line suggests this: ______________. 11. Question: The following regression model was fitted to sample data with 12 observations: y= 30 + 4.50x. What is the change in the predicted value of y for a unit change in the value? 12. Question: If the relationship between y and x is given by the equation y = 1.57 + 0.0407 x, the slope coefficient 0.0407 means this: ___________. 13. Question: In the equation y = m x + b, which represents a straight lime, m is the __________. 14. Question: A quality manager is developing a regression model to predict the total number of defects as a function of the day of week the item is produced. Production runs are done 10 hours a day, 7 days a week. The explanatory variable is _________. 15. Question: Given a set of paired data, {X, Y}, if Y is independent of X, you would expect that the correlation coefficient is _________. 16. Question: Determine the Pearson product-moment correlation coefficient for the following data. 17. Question: A numerical measure that indicates the strength of relationship between matched observations of two variables is -____________.