Exercise Problems on Chapter 13. Simple Regression Analysis This set of exercise problems has 23 problems, worth 25 points. 1. In simple regression analysis, the dependent variable is also known as a/an _____ variable and the independent variable is also known as a/an _____ variable. a. c. e. 2. b. d. response; explanatory all of the above In simple regression analysis, you will find _____ independent variable(s) and ____ dependent variable(s). a. d. 3. exogenous; endogenous to-be-determined; predetermined only (b) and (c) of the above one; one two; two Given the relationship of: b. e. one; two c. more than one; one two; one Y = 0 + 1 X + , 0 and 1are both called regression coefficients. More specifically, however, 0 is called a/an _____ and 1 is called a/an _____. a. c. e. 4. b. d. intercept; slope coefficient slope coefficient; slope coefficient The least-squares method for estimating regression coefficients is named as such because it tries to find the coefficient values by minimizing ______. a. b. c. e. 5. base; intercept slope coefficient; intercept Y-intercept; X-intercept the product of coefficients squared the sum of coefficients squared the sum of errors d. the sum of errors squared the sum of the dependent variable squared Given the following data of: Covariance between X and Y = SXY = 40 Variance of X = SX2 = 50 Number of observations = n = 10 X = 5 and Y = 8 the intercept value is _____ and the slope coefficient is _____. a. d. 6. 1.25; 1.75 X and Y are positively and directly related. as X decreases, Y decreases as well. as X increases, Y increases as well. all of the above is true. only (a) and (c) are true. X and Y are positively and directly related. as X decreases, Y increases as well. as X increases, Y decreases as well. X can determine the value of Y. none of the above. TSS = RSS + ESS RSS = TSS - ESS only (a) and (c) of the above b. d. ESS = TSS - RSS all of the above The regression sum of squares (RSS) is also called _____ variation and the error or residual sum of squares (ESS) is also called _____ variation. a. c. e. 10. c. The analysis-of-variance (ANOVA) table utilizes the partition of the various sums of squares. Given the total sum of squares (TSS), the regression sum of squares (RSS) and the error or residual sum of squares (ESS), which of the following relationship is true? a. c. e. 9. 0.8; 4 0.4; 0.08 If a slope coefficient is statistically equal to zero, it means that _____. a. b. c. d. e. 8. b. e. A positive slope coefficient means that _____. a. b. c. d. e. 7. 4; 0.8 1.75; 1.25 explained; unexplained total; uncertain only (c) and (d) of the above b. d. unexplained; explained good; bad Given the following data: The regression sum of squares (RSS) = 104 The error or residual sum of squares (ESS) = 56 The coefficient of determination is _____ and the correlation coefficient between X and Y is _____. a. d. 11. 0.65; 0.8062 standard deviation of Y variance of the predicted Y any of the above b. d. standard error of the estimate variance of Y errors (or residuals) are independent of one another. errors are normally distributed. errors are identically distributed and thus, have an equal variance. all of the above. only (a) and (b) of the above. errors (or residuals) are correlated an independent variable are correlated errors (or residuals) are not correlated an independent variable are not correlated errors (or residuals) are identical. Autocorrelation problem can be detected by the use of the _____. a. d. 15. c. Autocorrelation means that lagged values of _____ with one another. a. b. c. d. e. 14. 0.7338; 0.5384 0.65; 0.4225 Which of the following is an assumption of regression analysis? a. b. c. d. e. 13. b. e. A statistic that measures how much actual values of Y vary around the predicted values of Y on the basis of a regression equation is called the _____. a. c. e. 12. 0.5384; 0.7338 0.8062; 0.65 Z-statistic Durbin-Watson statistic b. e. t-statistic c. F-statistic either (b) or (d) of the above The significance test for a slope coefficient in an estimated regression equation can be done by the use of the _____. a. d. Z-statistic Durbin-Watson statistic b. e. t-statistic c. F-statistic either (a) or (b) of the above Given that the following demand relationship between the quantity demanded (Q) and its per-unit price (P) is estimated by a simple regression equation on the basis of 20 observations, answer Questions 16 through 21: Coefficient Intercept P 100 -5 Standard Error 45 2 p-value 0.03 0.005 The corresponding ANOVA table shows only the sums of squares as follows: Regression Error (or Residual) 16. Which of the following represents the estimated regression equation on the basis of the above information? a. d. 17. b. e. Q = 45 + 2P Q = 2.22 - 2.5P c. P = 100 - 5Q 0; 0 2.22; 2.5 b. e. 100; -5 2.22; -2.5 c. 45; 2 If you are to conduct a significance test for each of the estimated regression coefficients at a 5% significance level, you would conclude that the intercept term is _____ and the slope coefficient is _____. a. c. e. 19. Q = 100 - 5P P = 45 + 2Q If you are to conduct a significance test for the above regression coefficients at a 5% significance level, you would find the calculated t-value for the intercept to be _____ and that for the slope coefficient to be _____. a. d. 18. Sum of Squares 200 150 insignificant; insignificant significant; significant normal; normal b. d. insignificant; significant significant; insignificant If the calculated t- value for the slope coefficient is -1.9, you would find the table value of t to be _____ and thus, conclude to _____ the null hypothesis of the slope coefficient being equal to zero at the 5% significance level. a. d. 20. b. e. 1.7341; accept 2.1009; reject c. 1.7341; reject Based on the sums of squares given, the coefficient of determination is _____ and the corresponding calculated F-statistic is _____. a. d. 21. 1.7247; reject 2.1009; accept 0.5714; 24 0.4286; 1.333 b. e. 0.4286; 24 0.75; 1.333 c. 0.5714; 1.333 Given that an F-test is to be done for the joint significance of coefficients, you would find that the degrees of freedom for the numerator and the denominator are respectively _____ and _____. a. d. 1; 19 2; 19 b. e. 1; 18 2; 18 c. 2; 20 The following are worth 2 points each. 22. On the basis of 15 observations, you found a correlation coefficient between the inflation rate change (via the CPI) and your salary change to be 0.65. If you are to test the significance of this correlation coefficient, you would use a/an _____ and conclude that there is a/an _____ relationship between the inflation rate change and your salary change at a 5% significance level. a. c. e. 23. Z-statistic; significant t-statistic; significant F-statistic; significant b. d. Z-statistic; insignificant t-statistic; insignificant If the slope coefficient is found to be 5 in a simple regression equation and its standard error to be 3 on the basis of 10 observations, the 95% confidence interval for this slope coefficient lies between _____ and _____. a. d. -1; 11 -0.4375; 10.4375 b. e. -1.918; 11.918 0; 12 c. -0.5785; 10.5785