Exam 13: Simple Linear Regression

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: -True or False: Referring to Table 13-12,there is no evidence of positive autocorrelation if the Durbin-Watson test statistic is found to be 1.78.

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,what are the critical values of the Durbin-Watson test statistic using the 5% level of significance to test for evidence of positive autocorrelation?

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. -True or False: You give a pre-employment examination to your applicants.The test is scored from 1 to 100.You have data on their sales at the end of one year measured in dollars.You want to know if there is any linear relationship between pre-employment examination score and sales.An appropriate test to use is the t test of the population correlation coefficient.

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 degree(s)of freedom for the t test on whether the number of loan applications recorded affects the amount of time is (are)

TABLE 13-1 A large national bank charges local companies for using their services.A bank official reported the results of a regression analysis designed to predict the bank's charges (Y)-measured in dollars per month-for services rendered to local companies.One independent variable used to predict service charges to a company is the company's sales revenue (X)-measured in millions of dollars.Data for 21 companies who use the bank's services were used to fit the model: Y_i = β₀ + β₁X_i + ε_i The results of the simple linear regression are provided below. -Referring to Table 13-1,interpret the estimate of β₀,the Y-intercept of the line.

True or False: Regression analysis is used for prediction,while correlation analysis is used to measure the strength of the association between two numerical variables.

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,what is the standard deviation of the composite score around the regression line?

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.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 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 p-value for testing whether there is a linear relationship between revenue and the number of downloads at a 5% level of significance?

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 t test statistic when testing whether the number of customers who make a purchase affects weekly sales?

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 F test statistic to test whether the number of loan applications recorded affects the amount of time is ________.

The Y-intercept (b₀)represents the

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: -True or False: Referring to Table 13-11,the normality of error assumption appears to have been violated.

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 are the degrees of freedom of the t test statistic when testing whether the number of customers who make a purchase affects weekly sales?

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,generate the residual plot.

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. -The width of the prediction interval for the predicted value of Y is dependent on

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 both a 99% confidence interval estimate and a 99% prediction interval for X = 24.The confidence interval estimate would be the ________ ('wider' or 'narrower')of the two intervals.

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 least squares estimate of the Y-intercept 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 standard error of the estimated slope coefficient 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 regression sum of squares (SSR)is ________.