Exam 3 for Statistical Analysis for Business I | MSIT 3000, Exams of Business Management and Analysis

Download Exam 3 for Statistical Analysis for Business I | MSIT 3000 and more Exams Business Management and Analysis in PDF only on Docsity! 1. An economist would like to study the relationship between interest rates and the number of house loan (mortgage) applications. What would you expect regarding the correlation between interest rates and the number of mortgage applications? A. Negative correlation B. Positive correlation C. Close to 0 correlation D. Correlation cannot be computed ______________________________________________________________________________________ 2. What can be said about the correlation of the following two variables: A. Negative correlation B. Positive correlation C. Close to 0 correlation D. Correlation cannot be computed _____________________________________________________________________________________ 3. Insurance companies track claim histories so they can assess risk and set appropriate rates. The National Insurance Crime Bureau reports the most frequently stolen cars are Honda Accord, Honda Civic, and Toyota Camry, while the least frequently stolen cars are Ford Taurus, Pontiac Vibe and Buick LeSabre. What correlation should an insurance company expect between the type of car and the risk it will be stolen? A. Negative correlation B. Positive correlation C. Close to 0 correlation D. Correlation cannot be computed ______________________________________________________________________________________ 4. A business school collects data on the starting salary of its alumni, together with their GPA. It would like to provide this information to current students so that they can obtain realistic expectations about their salary after graduation. Which variable is the explanatory variable? A. Desired starting salary of current students B. Starting salary of alumni C. GPA of alumni D. Number of graduating students each year E. Number of alumni ______________________________________________________________________________________ 5. The table below shows the correlation coefficients between stock price, earnings per share (EPS) and price/ earnings (P/E) ratio for 19 publicly traded companies. Scatterplots for all pairs of variables show linear relationships. Which statement below is FALSE: Stock Price EPS EPS 0.88 PE 0.15 −0.72 A. There is a strong correlation between EPS and Stock Price B. The greater the increase in EPS, the greater the increase in Stock Price C. Stock Price and PE sometimes move in the same direction, sometimes in opposite directions D. If PE increases, EPS would usually decrease E. The weakest correlation is between PE and EPS ______________________________________________________________________________________ 1 QUESTIONS 6-8: A small, independent organic food store offers a variety of specialty coffees. To determine whether price has an effect on sales, the manager kept track of how many pounds of each variety of coffee were sold last month, together with the price. A scatterplot of the data as well as some of the summary statistics are shown below. salesy = 54.50 lbs ys = 18.33 lbs pricex = $8.75 xs = $3.63 r = −0.927 6. Is a linear regression model appropriate for this study? A. No, the quantitative condition is not satisfied B. No, the linearity condition is not satisfied C. No, there is an outlier present D. No, more than one condition is not satisfied E. Yes, the conditions are satisfied 7. Find the equation of the best fitting line. A. sales = 94.459 − 4.681 * price/pound B. sales = 13.541 − 4.681 * price /pound C. sales = 18.778 − 0.184 * price/pound D. sales = −1.278 − 0.184 * price/pound E. sales = 56.110 − 0.184 * price/pound 8. Which statement below is true: A. 92.7% of the variation in pounds sold can be accounted for on the basis of price/pound B. 92.7% of the variation in price/pound can be accounted for on the basis of pounds sold C. 85.9% of the variation in pounds sold can be accounted for on the basis of price/pound D. 85.9% of the variation in price/pound can be accounted for on the basis of pounds sold E. None of the above ______________________________________________________________________________________ 2 QUESTIONS 15-17: A quality control officer wanted to analyze the effect of training on solving problems. 10 workers were selected at random. Information was recorded on how many hours of training they had received, as well as how long it took them to solve a particular problem. A scatterplot showed a linear relationship, and residual plots indicated the other conditions were satisfied. The following regression output was obtained: Coefficients P-value Intercept 30.729 0.062 Training −1.836 0.014 15. Which hypotheses should be tested to see if there is a linear relationship between trouble shooting time and training time? A. H0: β0 = 0, HA: β0 ≠ 0 B. H0: β1 = 0, HA: β1 ≠ 0 C. H0: β1 = β0 = 0, HA: at least one of β0, β1 different from 0 D. H0: β0 = 0, HA: β0 > 0 E. H0: β1 = 0, HA: β1 < 0 16. Which of the following statements are true: I. For α = 0.01, you would not conclude a linear relationship between training and troubleshooting time II. For α = 0.02, you would not conclude a linear relationship between training and troubleshooting time III. For α = 0.05, you would conclude a linear relationship between training and troubleshooting time A. III only B. I and II only C. I and III only D. II and III only E. I, II and III 17. The quality control officer would like to make a 99% confidence interval for the slope. What can be said about this interval? A. A 99% confidence interval for the slope would contain 0 B. A 99% confidence interval for the slope would not contain 0 C. It is not possible to predict whether the interval would contain 0 without knowing the standard error D. It is not possible to predict whether the interval would contain 0 without knowing the value of t* E. It is not possible to predict whether the interval would contain 0 without knowing the value of β1. ______________________________________________________________________________________ 5 QUESTIONS 18-21: Many companies try to reduce employee turnover – the rate at which employees leave the company and have to be replaced. A study of 20 companies was done with the intent of predicting turnover rate on the basis of average salary, average bonus, and average trust score (a questionnaire taken by employees regarding their level of trust in the employer). The following output was obtained: Coefficient Standard Error Test Statistic P-value Intercept 12.1005 0.7826 15.46 <0.001 Salary −0.7149 0.197 −3.63 0.0015 Bonus 0.0531 0.018 2.95 0.0024 Trust −0.4382 0.2571 −1.704 0.1246 ANOVA DF SS MS F Model ? 262.73 ? ? Error ? 67.27 ? Total ? 330.00 18. Which of the following is closest to the value of the F-statistic? A. 3.906 B. 14.646 C. 15.622 D. 20.830 E. 22.132 19. Which hypotheses should be tested to determine if the overall model is useful? A. H0: β0 = βsalary = βbonus = βtrust = 0; HA: β0 ≠ βsalary ≠ βbonus ≠ βtrust ≠ 0 B. H0: β0 = βsalary = βbonus = βtrust = 0; HA: at least one of the β’s are different from 0s are different from 0 C. H0: b0 = bsalary = bbonus = btrust = 0; HA: at least one of the b’s are different from 0s are different from 0 D. H0: βsalary = βbonus = βtrust = 0; HA: at least one of the β’s are different from 0s are different from 0 E. H0 : βsalary = βbonus = βtrust = 0; HA: βsalary < 0, βbonus > 0, βtrust < 0 20. The coefficient for Bonus is positive. What does this imply? A. The higher the bonus, the more likely an employee is to leave B. The lower the bonus, the more likely an employee is to leave C. The higher the bonus for a fixed level of salary and trust, the more likely an employee is to leave D. The lower the bonus for a fixed level of salary and trust, the more likely an employee is to leave E. Bonus is not a significant predictor for α = 0.05, so doesn’s are different from 0t matter whether it is positive or negative 21. Which predictor variables are useful in predicting employee turnover, for α = 0.05? A. Salary only B. Salary and Bonus only C. Trust only D. Salary, Bonus and Trust E. None of the variables ______________________________________________________________________________________ 6 QUESTIONS 22-26: Which factors affect LCD TV sales? Sales data (number of units sold) for a particular model were collected from n electronics stores, together with the price of the unit at each store and the amount of advertizing spent by each store. Output from a multiple regression model is shown below Coefficient Standard Error Test Statistic P-value Intercept 90.19 25.08 3.60 0.0012 Price −0.0306 0.0101 −3.03 0.0110 Advertizing 3.0926 0.3680 8.40 <0.001 ANOVA DF SS MS F P-value Model ? 16477.3 8238.7 32.54 <0.001 Error 12 3038.0 253.2 Total ? 19515.3 22. What is the sample size, n? A. 12 B. 13 C. 14 D. 15 E. 16 23. What is the value of se, the standard deviation of the model? A. 15.91 B. 37.33 C. 55.12 D. 90.77 E. 253.2 24. What is the conclusion of the hypothesis test to determine if the overall model is useful, for α = 0.01? A. There is sufficient evidence that the model is not useful B. There is sufficient evidence that the model is useful C. There is conflicting evidence because some predictors are useful while others are not. D. There is insufficient evidence that the model is useful E. There is insufficient evidence that all of the predictors are useful. 25. Find a 95% confidence interval for βprice . A. (−0.0526, −0.0086) B. (−0.0524, −0.0088) C. (−0.0523, −0.0089) D. (−0.0504, −0.0108) E. (−3.0520, −3.0079) 26. Suppose a third predictor variable is added to the model: the number of advertisements shown by each store. This variable makes very little additional contribution to predicting the number of units sold, i.e. it increases the accuracy of the predictions by only a very small amount. Which statement is correct: A. R2 will decrease but R2-adjusted will increase. B. R2 will increase but R2-adjusted will decrease. C. R2 and R2-adjusted will both increase. D. R2 and R2-adjusted will both decrease. E. The changes in R2 and R2-adjusted cannot be predicted. 7