(ii) Scan your answer sheets INTO ONE FILE only, and submit it in the drop-box.

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1 FINAL EXAM ** Two different ways to submit your answer sheet (i) Use MS-Word and place it in a drop-box. (ii) Scan your answer sheets INTO ONE FILE only, and submit it in the drop-box. Deadline: December 1 th, 011 (Monday) by noon. Part I :True / False 1. The usual objective of regression analysis is to predict estimate the value of one variable when the value of another variable is known.. Correlation analysis is concerned with measuring the strength of the relationship between two variables. 3. The term e i in the simple linear regression model indicates the amount of change in Y for a unit change in X. 4. In the sample regression equation y = a + bx, b is the slope of the regression line. 5. The coefficient of determination can assume any value between -1 and In the least squares model, the explained sum of squares is always smaller than the regression sum of squares. 7. The sample correlation coefficient and the sample slope will always have the same sign. 8. Given the sample regression equation y = x, we know that in the sample X and Y are inversely related. 9. Given the sample regression equation y = 5 6x, we know that when X =, Y = An important relationship in regression analysis is ( Yi Y) = ( Ŷ Y) (Yi Ŷ). 11. Regression analysis is concerned with the form of the relationship among variables, whereas correlation analysis is concerned with the strength of the relationship. 1

2 1. The correlation coefficient indicates the amount of change in Y when X change by one unit. 13. In simple linear regression analysis, when the slope is equal to zero, the independent variable does not explain any of the variability in the dependent variable. 14. One of the purposes of regression analysis is to estimate a mean of the independent variable for given values of the dependent variable. 15. The variable that can be manipulated by the investigator is called the independent variable. 16. When b = 0, X and Y are not related. 17. If zero is contained in the 95% confidence interval for b, we may reject H o : b = 0 at the 0.05 level of significance. 18. If in a regression analysis the explained sum of squares is 75 and the unexplained sum of square is 5, r = In general, the smaller the dispersion of observed points about a fitted regression line, the larger the value of the coefficient of determination. 0. When small values of Y tend to be paired with small values of X, the relationship between X and Y is said to be inverse. Part II Select the correct answer for the following questions 1. The variable about which the investigator wishes to make predictions or estimates is called the a. dependent variable b. unit of association c. independent variable d. discrete variable. In regression analysis, the quantity that gives the amount by which Y changes for a unit change in X is called the a. coefficient of determination b. slope of the regression line c. Y intercept of the regression line d. correlation coefficient 3. In the equation y = b 0 +b 1 (x), b 0 is the a. coefficient of determination b. slope of the regression line c. y intercept of the regression line d. correlation coefficient

3 4. In the equation y = b 0 + b 1 (x), b 1 is the a. coefficient of determination b. slope of the regression line c. y intercept of the regression line d. correlation coefficient 5. In regression and correlation analysis, the measure whose values are restricted to the range 0 to 1, inclusive, is the a. coefficient of determination b. slope of the regression line c. y intercept of the regression line d. correlation coefficient 6. In regression and correlation analysis, the measure whose values are restricted to the range -1 to +1, inclusive, is the a. coefficient of determination b. slope of the regression line c. y intercept of the regression line d. correlation coefficient 7. The quantity ( Y i Yˆ) is called the sum of square. a. least b. explained c. total d. unexplained 8. If, in the regression model, b = 0, we say there is linear relationship between X and Y. a. an inverse b. a significant c. a direct d. no 9. If, in the regression model, b is negative, we say there is linear relationship between X and Y. a. an inverse b. a significant c. a direct d. no 30. The sum of square is a measure of the total variability in the observed values of Y that is accounted for by the linear relationship between the observed values of X and Y. a. unexplained b. total c. error d. explained 31. If two variables are not related, we know that. a. their correlation coefficient is equal to zero. b. the variability in one of them cannot be explained by the other. c. the slope of the regression line for the two variables is equal to zero. d. all of the above statements are true. 3. In simple linear regression analysis, if the correlation coefficient is equal to 1.0,. a. the slope is equal to 1.0 b. all the variability in the dependent variable is explained by the independent variable. c. the y intercept is equal to 1.0 3

4 d. the relationship between the two variables can be described as a bivariable normal distribution. 33. The following results were obtained from a simple linear regression analysis. Total sum of square = Unexplained sum of square = 0.5. The coefficient of determination is a b c d The following results were obtained as part of a simple linear correlation analysis: Y = x regression sum of squares = Error sum of squares = Total sum of squares = The sample correlation coefficient is a b c d The following equation describes the relationship between output and labor input at a sample of work stations in a manufacturing plant: Y = x. Suppose, for a selected work station, the labor input is 5. The predicted output is. a b..35 c..0 d In regression and correlation analysis, the entity on which sets of measurements are taken is called the. a. dependent variable b. independent variable c. unit of association d. discrete variable is called the sum of squares. a. least b. total c. explained d. unexplained 37. The quantity Y ˆ Y 38. If, in the regression model, b is positive, we say there is linear relationship between X and Y. a. an inverse b. a direct c. a significant d. no 39. If, as X increase, Y tends to increase, we say there is linear relationship between X and Y. a. an inverse b. a direct c. a significant d. no 40. The explained sum of squares divided by the total sum of squares yield the. a. F statistic b. total mean square c. p value d. coefficient of multiple determination 4

5 Part III: **All work must be shown (step by step) in order to receive credit** 41. Find the table value and make a decision concerning H o using the following data: Support your decision. a. Ha: µ 10; α = 0.05, n = 15; t = 1.95 b. Ha: µ > 10; α = 0.10, n = 8; t = 3. c. Ha: µ < 10; α = 0.05, n = 17; t = -1.6 d. Ha: µ 10; α = 0.05, n = 14; t =.54 e. Ha: µ > 10; α = 0.10, n = 0; t = 1.54 f. Ha: µ < 10; α = 0.10, n = ; t =

6 4. Find the equation of the least squares line relating Y to X on the following data. x y Σx = 10 Σy = 10 Σxy = 18 Σx =30 Σy =36 Yˆ = 6 1.4x, Yˆ = 4.6, 3., 1.8, 0.4. Report the calculated values using the following formulas = y b0 y b1 xy n k = n ˆ y y = n y y 1 b n x x 1 r = SST n k Hint: SST = y n y 6

7 43. Calculate r for the following sets of data: a) y y 10 and y ˆ y = 140 b) y y 100 and y ŷ = 10 c) y ˆ y 75 and y ŷ = A large hotel purchased 00 new color televisions several months ago: 80 of one brand and 60 of each of two other brands. Records were kept for each set as to how many service calls were required, resulting in the table that follows. Number of TV Brand Total Service Calls Sony Toshiba Sanyo None One Two or more Total Assume the TV sets are random samples of their brands. With 5% risk of Type I error, test for an association between TV brand and the number of service calls. 7

8 1. Is the value significant at 5% level of significant?. Write the conclusion for this question 45. Determining the regression equation for the information provide below and calculate the coefficient of correlation. X Y Explain the theoretical meaning of b o, b 1, S b 1, and S e. 8

9 46. Fill in the missing values in following ANOVA table Source df SS MS F Factor Error 637 Total 5 a. In the above ANOVA table, is the factor significant at 5% level of significant? Answer 47. Fill in the missing values in following ANOVA table Source df SS MS F Factor 3.4 Error 17 Total a. In the above ANOVA table, is the factor significant at 5% level of significant? Answer 48. Fill in the missing values in following ANOVA table Source df SS MS F Factor Error 16 Total a. In the above ANOVA table, is the factor significant at 5% level of significant? Answer 9

10 49. 1) Computer output: Coefficients Std. Error t-stat P-value Intercept Price Advertising ANOVA df SS MS F Significance F Regression Residual Total S e = R-sq = R-sq(adj) = a) Write and interpret the multiple regression equation. b) Does the model with Price and Advertising contribute to the prediction of Y? Use a 0.05 significance level. c) Which independent variable appears to be the best predictor of sales? Explain. d) What is the number of observations used in this study? 10

11 e) Assuming that the coefficient on Advertising has H a : B1 > 0, what statistical decision should be made at 5% level. f) What is the standard error of estimate? Can you use this statistic to assess the model s fit? If so, how? g) What is the coefficient of determination, and what does it tell you about the regression model? h) What is the coefficient of determination, adjusted for degrees of freedom? What do this statistic and the statistic referred to in part (g) tell you about how well this model fits that data. i) Test the overall utility of the model. What does the p-value of the test statistic tell you? 11

12 50. 1

13 Use the printout above answer the questions. a. Is the relationship between working capital and net sales statistically significant? b. What is the coefficient of determination? What do you conclude in terms of the variables? c. What is the correlation coefficient? What do you conclude in terms of the variables? d. What is the standard error of estimate? e. What is the regression equation? Interpret the regression equation. f. If working capital equals $100,000 what is the estimate for net sales? 13

14 Please Fill in the blanks. 51) The purpose of hypothesis testing is to aid the manager or researcher in reaching a (an) concerning a (an) by examining the data contained in a (an) from that. 5) A hypothesis may be defined simply as. 53) There are two statistical hypotheses. They are the hypothesis and the hypothesis. 54) The statement of what the investigator is trying to conclude is usually placed in the hypothesis. 55) The hypothesis is the hypothesis that is tested. 56) If the null hypothesis is not rejected, we conclude that the alternative. 57) If the null hypothesis is not rejected, we conclude that the null hypothesis. 58) A Type I error occurs when the investigator. 59) A Type II error occurs when the investigator. 14