Exam 12: Simple Linear Regression

Which of the following assumptions concerning the probability distribution of the random error term is stated incorrectly?

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 regression sum of squares (SSR)is ________.

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 coefficient of determination?

TABLE 12-13 In this era of tough economic conditions, voters increasingly ask the question: "Is the educational achievement level of students dependent on the amount of money the state in which they reside spends on education?" The partial computer output below is the result of using spending per student ($) as the independent variable and composite score, which is the sum of the math, science, and reading scores, as the dependent variable on 35 states that participated in a study. The table includes only partial results. -Referring to Table 12-13, the p-value of the measured t test statistic to test whether composite score depends linearly on spending per student is ________.

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. -Referring to Table 12-9, the estimated change in mean salary (in thousands of dollars)as a result of spending an extra hour per day studying 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. The p-value of the test is ________.

TABLE 12-13 In this era of tough economic conditions, voters increasingly ask the question: "Is the educational achievement level of students dependent on the amount of money the state in which they reside spends on education?" The partial computer output below is the result of using spending per student ($) as the independent variable and composite score, which is the sum of the math, science, and reading scores, as the dependent variable on 35 states that participated in a study. The table includes only partial results. -Referring to Table 12-13, the p-value of the measured F test statistic to test whether spending per student affects composite score 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, what are the lower and upper limits of the 95% confidence interval estimate for population slope?

TABLE 12-13 In this era of tough economic conditions, voters increasingly ask the question: "Is the educational achievement level of students dependent on the amount of money the state in which they reside spends on education?" The partial computer output below is the result of using spending per student ($) as the independent variable and composite score, which is the sum of the math, science, and reading scores, as the dependent variable on 35 states that participated in a study. The table includes only partial results. -Referring to Table 12-13, the conclusion on the test of whether spending per student affects composite score using a 5% level of significance is:

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 critical values of the test are dL = ________, and dU = ________.

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, the null hypothesis that there is no linear relationship between revenue and the number of downloads should be rejected at a 5% level of significance.

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 standard error of the estimate is ________.

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, construct a 95% prediction interval for the weekly sales of a store that has 600 purchasing customers.

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 total sum of squares (SST)is ________.

TABLE 12-8 It is believed that GPA (grade point average, based on a four-point scale) should have a positive linear relationship with ACT scores. Given below is the Microsoft Excel output for predicting GPA using ACT scores based a data set of eight randomly chosen students from a Big Ten university. -Referring to Table 12-8, what is the predicted value of GPA when ACT = 20?

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, the homoscedasticity of error assumption appears to have been violated.

The slope (b₁)represents

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 standard error of estimate is ________.

The Y-intercept (b₀)represents the

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, construct a 95% confidence interval for the mean weekly sales when the number of customers who make purchases is 600.