Exam 13: Simple Linear Regression

TABLE 13-2 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 6 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: -True or False: The Chancellor of a university has commissioned a team to collect data on students' GPAs and the amount of time they spend bar hopping every week (measured in minutes).He wants to know if imposing much tougher regulations on all campus bars to make it more difficult for students to spend time in any campus bar will have a significant impact on general students' GPAs.His team should use a t test on the slope of the population regression.

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 prediction for the number of job offers for a person with 2 coop jobs 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 total sum of squares (SST)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 90% confidence interval for the mean change in the amount of time needed as a result of recording one additional loan application 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,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 confidence interval is from ________ to ________.

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 total sum of squares (SST)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,there is sufficient evidence that revenue and the number of downloads are linearly related at a 5% level of significance.

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 error or residual sum of squares (SSE)is ________.

TABLE 13-2 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 6 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 13-2,what percentage of the total variation in candy bar sales is explained by prices?

If the residuals in a regression analysis of time-ordered data are not correlated,the value of the Durbin-Watson D statistic should be near ________.

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 denominator of the test statistic is .The value of in this sample 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: -True or False: Referring to Table 13-10,it is inappropriate to compute the Durbin-Watson statistic and test for autocorrelation in this case.

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: -Referring to Table 13-5,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 d_L = ________,and d_U = ________.

TABLE 13-2 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 6 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 13-2,what is the standard error of the estimate,S_YX,for the data?

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,construct a 95% confidence interval for the change in mean weekly sales when the number of customers who make purchases increases by one.

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,what are the decision and conclusion on testing whether there is any linear relationship at 1% level of significance between GPA and ACT scores?

True or False: The Durbin-Watson D statistic is used to check the assumption of normality.

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 regression mean square (MSR)of the above regression 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.The value of the test statistic 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: -True or False: Referring to Table 13-10,the value of the F test statistic equals the square of the t test statistic when testing whether the number of customers who make purchases is a good predictor for weekly sales.