Exam 13: Simple Linear Regression

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, 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 regression sum of squares (SSR) 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 degrees of freedom of the t test statistic when testing whether the number of customers who make a purchase affects weekly sales?

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 is the correct alternative hypothesis for testing whether there is a linear relationship between revenue and the number of downloads?

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. At a level of significance of 0.01, the null hypothesis should be ________ (rejected or not rejected).

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: Yᵢ = β₀ + β₁Xi + Eᵢ The results of the simple linear regression are provided below. -Referring to Table 13-1, interpret the p-value for testing whether β₁ exceeds 0.

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 least squares estimate of the Y-intercept 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 the mean change in revenue as a result of a one thousand increase in the number of downloads?

TABLE 13-7 An investment specialist claims that if one holds a portfolio that moves in the opposite direction to the market index like the S&P 500, then it is possible to reduce the variability of the portfolio's return. In other words, one can create a portfolio with positive returns but less exposure to risk. A sample of 26 years of S&P 500 index and a portfolio consisting of stocks of private prisons, which are believed to be negatively related to the S&P 500 index, is collected. A regression analysis was performed by regressing the returns of the prison stocks portfolio (Y) on the returns of S&P 500 index (X) to prove that the prison stocks portfolio is negatively related to the S&P 500 index at a 5% level of significance. The results are given in the following Excel output. Note: 2.94942E-07 = 2.94942*10⁻⁷ -Referring to Table 13-7, to test whether the prison stocks portfolio is negatively related to the S&P 500 index, the p-value of the associated test statistic 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 estimate is ________.

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 standard error of the estimate 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, which of the following is the correct interpretation for the coefficient of determination?

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 both a 95% confidence interval estimate and a 95% prediction interval for X = 2. The confidence interval estimate would be the wider 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 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 ________.

The sample correlation coefficient between X and Y is 0.375. It has been found out that the p-value is 0.256 when testing H₀: ρ = 0 against the two-sided alternative H₁: ρ ≠ 0. To test H₀: ρ = 0 against the one-sided alternative H₁: ρ < 0 at a significance level of 0.1, the p-value is

Referring to Table 13-2, to test that the regression coefficient, β₁, is not equal to 0, what would be the critical values? Use α = 0.05.

If you wanted to find out if alcohol consumption (measured in fluid oz.) and grade point average on a 4-point scale are linearly related, you would perform a

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: Note: 4.3946E-15 is 4.3946 × -Referring to Table 13-12, there is sufficient evidence that the amount of time needed linearly depends on the number of loan applications at a 1% level of significance.

The slope (b₁) represents

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 two 95% confidence interval estimates. One is for the mean number of job offers received by students who have had exactly one cooperative education job and one for people who have had two. The confidence interval for students who have had one cooperative education job would be the wider of the two intervals.