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: -Referring to Table 13-12,to test the claim that the mean amount of time depends positively on the number of loan applications recorded against the null hypothesis that the mean amount of time does not depend linearly on the number of invoices processed,the p-value of the test statistic 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,if the price of the candy bar is set at $2,the estimated mean sales will be

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 appears to be autocorrelation in the residuals.

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 coefficient of correlation is ________.

Based on the residual plot below,you will conclude that there might be a violation of which of the following assumptions?

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 coefficient of determination 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,predict the amount of time it would take to process 150 invoices.

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 assumptions appears to have been violated?

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 composite score depends linearly on spending per student using a 10% level of significance is to ________ (reject or not reject) .

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 t test statistic and F test statistic should be the same when testing whether the number of customers who make purchases is a good predictor for weekly sales.

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 coefficient of determination is ________.

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

If the plot of the residuals is fan shaped,which assumption is 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: -True or False: Referring to Table 13-10,93.98% of the total variation in weekly sales can be explained by the variation in the number of customers who make purchases.

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 estimated mean change in the sales of the candy bar if price goes up by $1.00?

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: A zero population correlation coefficient between a pair of random variables means that there is no linear relationship between the random variables.

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,to test whether a change in price will have any impact on sales,what would be the critical values? Use α = 0.05.

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 Durbin-Watson statistic is inappropriate for this data set.

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% prediction interval estimate for the number of job offers received by students who have had exactly one cooperative education job.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: -True or False: Referring to Table 13-12,there is a 95% probability that the mean amount of time needed to record one additional loan application is somewhere between 0.0109 and 0.0143 hours.