Exam 13: Simple Linear Regression

TABLE 13-8 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 Excel output for predicting GPA using ACT scores based on a data set of 8 randomly chosen students from a Big-Ten university. -Referring to Table 13-8,the interpretation of the coefficient of determination in this regression is

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 σ,the standard deviation of the random error term (standard error of the estimate)in the model.

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% prediction interval for the sales made by a broker who has brought into the firm 18 new clients.The prediction interval is from ________ to ________.

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 error sum of squares (SSE)of the above regression 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 are the values of the estimated intercept and slope?

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 n a 99% prediction interval for the sales made by a broker who has brought into the firm 18 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 value of the measured t test statistic to test whether composite score depends linearly on spending per student 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 p-value of the F test statistic when testing whether the number of customers who make purchases is a good predictor for 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,the residual plot indicates possible violation of which assumptions?

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 conclusion on the test of whether spending per student affects composite score using a 5% level of significance is that

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 0.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,suppose the director of cooperative education wants to construct a 95% confidence-interval estimate for the mean number of job offers received by students who have had exactly one cooperative education job.The t critical value she would use 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: -True or False: Referring to Table 13-11,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 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: -The coefficient of determination (r²⁾ tells you

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 value of the test statistic is ________.

TABLE 13-8 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 Excel output for predicting GPA using ACT scores based on a data set of 8 randomly chosen students from a Big-Ten university. -Referring to Table 13-8,the value of the measured test statistic to test whether there is any linear relationship between GPA and ACT 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?

The least squares method minimizes which of the following?

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 p-value for testing whether β₁exceeds 0.

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: -True or False: Referring to Table 13-10,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.