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Exam 12: Simple Linear Regression

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Question 71

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TABLE 12-3 The director of cooperative education at a state college wants to examine the effect of cooperative education job experience on marketability in the work place. She takes a random sample of four students. For these four, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below. -Referring to Table 12-3, suppose the director of cooperative education wants to construct a 95% prediction interval for the number of job offers received by a student who has had exactly two cooperative education jobs. The t critical value she would use is ________.

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Question 72

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TABLE 12-4 The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows. -Referring to Table 12-4, the managers of the brokerage firm wanted to test the hypothesis that the population slope was equal to 0. The value of the test statistic is ________.

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Question 73

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TABLE 12-10 The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousand of dollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the following results: -Referring to Table 12-10, the null hypothesis for testing whether the number of customers who make a purchase effects weekly sales cannot be rejected if a 1% probability of committing a Type I error is desired.

TABLE 12-4 The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows. -Referring to Table 12-4, the managers of the brokerage firm wanted to test the hypothesis that the number of new clients brought in had a positive impact on the amount of sales generated. For a test with a level of significance of 0.01, the null hypothesis should be rejected if the value of the test statistic is ________.

TABLE 12-7 An investment specialist claims that if one holds a portfolio that moves in the opposite direction to the market index like the S&P 500, then it is possible to reduce the variability of the portfolio's return. In other words, one can create a portfolio with positive returns but less exposure to risk. A sample of 26 years of S&P 500 Index and a portfolio consisting of stocks of private prisons, which are believed to be negatively related to the S&P 500 Index, is collected. A regression analysis was performed by regressing the returns of the prison stocks portfolio (Y) on the returns of S&P 500 Index (X) to prove that the prison stocks portfolio is negatively related to the S&P 500 Index at a 5% level of significance. The results are given in the following Microsoft Excel output. Note: 2.94942E-07 = 2.94942 * 10-7 -Referring to Table 12-7, to test whether the prison stocks portfolio is negatively related to the S&P 500 Index, the measured value of the test statistic is ________.

TABLE 12-4 The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows. -Referring to Table 12-4, the managers of the brokerage firm wanted to test the hypothesis that the population slope was equal to 0. At a level of significance of 0.01, the null hypothesis should be ________ (rejected or not rejected).

TABLE 12-10 The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousand of dollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the following results: -Referring to Table 12-10, what is the value of the F test statistic when testing whether the number of customers who make purchases is a good predictor for weekly sales?

TABLE 12-4 The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows. -Referring to Table 12-4, the managers of the brokerage firm wanted to test the hypothesis that the number of new clients brought in had a positive impact on the amount of sales generated. The value of the test statistic is ________.

TABLE 12-4 The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows. -Referring to Table 12-4, the prediction for the amount of sales (in $1,000s)for a person who brings 25 new clients into the firm is ________.

TABLE 12-2 A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses six small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below: . -Referring to Table 12-2, what is the coefficient of correlation for these data?

TABLE 12-9 It is believed that, the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation. Given below is the Microsoft Excel output for predicting starting salary (Y) using number of hours spent studying per day (X) for a sample of 51 students. NOTE: Only partial output is shown. Note: 2.051E-05 = 2.051 * 10-0.5 and 5.944E-18 = 5.944 * 10-18. -A zero population correlation coefficient between a pair of random variables means that there is no linear relationship between the random variables.

Testing for the existence of correlation is equivalent to

When r = -1, it indicates a perfect relationship between X and Y.

TABLE 12-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 12-11, which of the following assumptions appears to have been violated?

TABLE 12-4 The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows. -Referring to Table 12-4, the managers of the brokerage firm wanted to test the hypothesis that the population slope was equal to 0. At a level of significance of 0.01, the decision that should be made implies that ________ (there is a or there is no)linear dependent relationship between the independent and dependent variables.

TABLE 12-3 The director of cooperative education at a state college wants to examine the effect of cooperative education job experience on marketability in the work place. She takes a random sample of four students. For these four, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below. -Referring to Table 12-3, the director of cooperative education wanted to test the hypothesis that the population slope was equal to 3.0. The p-value of the test is between ________ and ________.

TABLE 12-2 A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses six small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below: . -The residual represents the discrepancy between the observed dependent variable and its ________ value.

TABLE 12-5 The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel to analyze the last four years of quarterly data (i.e., n = 16) with the following results: -Referring to Table 12-5, the partner wants to test for autocorrelation using the Durbin-Watson statistic. Using a level of significance of 0.05, the decision he should make is:

TABLE 12-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: -Referring to Table 12-11, predict the revenue when the number of downloads is 30 thousands.

TABLE 12-5 The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel to analyze the last four years of quarterly data (i.e., n = 16) with the following results: -The coefficient of determination (r²) tells you