Exam 13: Simple Linear Regression

TABLE 13-4 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 13-4,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 13-6 The following Excel tables are obtained when "Score received on an exam (measured in percentage points)" (Y)is regressed on "percentage attendance" (X)for 22 students in a Statistics for Business and Economics course. -Referring to Table 13-6,which of the following statements is true?

TABLE 13-11 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 13-11,which of the following is the correct alternative hypothesis for testing whether there is a linear relationship between revenue and the number of downloads?

TABLE 13-11 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 13-11,predict the revenue when the number of downloads is 30 thousands.

TABLE 13-9 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 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^-05 and 5.944E - 18 = 5.944 ∗ 10^-18. -Referring to Table 13-9,the value of the measured t test statistic to test whether mean SALARY depends linearly on HOURS is

TABLE 13-11 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 13-11,what is the standard deviation around the regression line?

TABLE 13-13 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 13-13,the value of the F test on whether spending per student affects composite score is ________.

TABLE 13-10 The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousands 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 13-10,what is the value of the coefficient of correlation?

In a simple linear regression problem,r and b₁

TABLE 13-4 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 13-4,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 p-value of the test is ________.

TABLE 13-9 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 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^-05 and 5.944E - 18 = 5.944 ∗ 10^-18. -Referring to Table 13-9,the 90% confidence interval for the average change in SALARY (in thousands of dollars)as a result of spending an extra hour per day studying is

TABLE 13-4 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 13-4,the managers of the brokerage firm wanted to test the hypothesis that the number of new clients brought in did not affect the amount of sales generated.The value of the test statistic is ________.

TABLE 13-5 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 4 years of quarterly data with the following results: -If the Durbin-Watson statistic has a value close to 0,which assumption is violated?

TABLE 13-4 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 13-4,suppose the managers of the brokerage firm want to construct a 99% confidence interval estimate for the mean sales made by brokers who have brought into the firm 24 new clients.The t critical value they would use is ________.

TABLE 13-13 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 13-13,the decision on the test of whether spending per student affects composite score using a 5% level of significance is to ________ (reject or not reject) .

TABLE 13-4 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 13-4,the standard error of estimate is ________.

TABLE 13-3 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 4 students.For these 4,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 13-3,the standard error of estimate is ________.

TABLE 13-12 The manager of the purchasing department of a large saving and loan organization would like to develop a model to predict the amount of time (measured in hours)it takes to record a loan application.Data are collected from a sample of 30 days,and the number of applications recorded and completion time in hours is recorded.Below is the regression output: -Referring to Table 13-12,the p-value of the measured t test statistic to test whether the number of loan applications recorded affects the amount of time is ________.

TABLE 13-3 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 4 students.For these 4,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 13-3,the director of cooperative education wanted to test the hypothesis that the population slope was equal to 3.0.For a test with a level of significance of 0.05,the null hypothesis should be rejected if the value of the test statistic is ________.

TABLE 13-3 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 4 students.For these 4,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 13-3,the least squares estimate of the Y-intercept is ________.