Exam 13: Simple Linear Regression

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

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 percentage of the total variation in candy bar sales explained by the regression model?

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 (i.e., n = 16) with the following results: -Referring to Table 13-5, the correlation coefficient is ________.

Testing for the existence of correlation is equivalent 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 director of cooperative education wanted to test the hypothesis that the population slope was equal to 3.0. The p-value of the test is between ________ and ________.

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

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

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 13-4 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 ________.

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 critical value at 5% level of significance of the F test on whether spending per student affects composite score 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 are the lower and upper limits of the 95% confidence interval estimate for population slope?

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, the p-value of the measured t test statistic to test whether composite score depends linearly on spending per student is ________.

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 13-4 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 ________.

Referring to Table 13-2, what is the standard error of the regression slope estimate, ?

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) H₀.

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 F test statistic 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 regression sum of squares (SSR) is ________.

If the correlation coefficient (r) = 1.00, then