Exam 12: Simple Linear Regression

TABLE 12-3 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 four students. For these four, 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 12-3, the regression sum of squares (SSR)is ________.

TABLE 12-1 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: Y1 - β0 + β1X1 + εi The results of the simple linear regression are provided below. Y = -2,700 + 20 X, SYX = 65, two-tail p-value = 0.034 (for testing β1) -Referring to Table 12-1, interpret the estimate of β₀, the Y-intercept of the line.

TABLE 12-3 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 four students. For these four, 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 12-3, 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 confidence interval is from ________ to ________.

TABLE 12-12 The manager of the purchasing department of a large savings 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 x 10-15. -Referring to Table 12-12, the degrees of freedom for the t test on whether the number of loan applications recorded affects the amount of time are

TABLE 12-9 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 Microsoft 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 * 10-0.5 and 5.944E-18 = 5.944 * 10-18. -Referring to Table 12-9, the degrees of freedom for the F test on whether HOURS affects SALARY are ________.

TABLE 12-11 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 12-11, there appears to be autocorrelation in the residuals.

TABLE 12-5 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 four years of quarterly data (i.e., n = 16) with the following results: -Referring to Table 12-5, the estimates of the Y-intercept and slope are ________ and ________, respectively.

TABLE 12-4 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 12-4, the managers of the brokerage firm 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 12-3 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 four students. For these four, 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 12-3, the total sum of squares (SST)is ________.

TABLE 12-4 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 12-4, the managers of the brokerage firm wanted to test the hypothesis that the number of new clients brought in did not affect the amount of sales generated. The value of the test statistic is ________.

TABLE 12-3 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 four students. For these four, 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 12-3, the coefficient of correlation 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 ________.

In a simple linear regression problem, r and b₁

TABLE 12-11 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 12-11, what is the value of the test statistic for testing whether there is a linear relationship between revenue and the number of downloads?

TABLE 12-11 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 12-11, which of the following is the correct interpretation for the slope coefficient?

TABLE 12-4 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 12-4, 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 12-13 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 12-13, the value of the measured t test statistic to test whether composite score depends linearly on spending per student is ________.

TABLE 12-9 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 Microsoft 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 * 10-0.5 and 5.944E-18 = 5.944 * 10-18. -Referring to Table 12-9, to test the claim that SALARY depends positively on HOURS against the null hypothesis that SALARY does not depend linearly on HOURS, the p-value of the test statistic is ________.

TABLE 12-10 The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousand 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 12-10, the mean weekly sales will increase by an estimated $0.01 for each additional purchasing customer.

TABLE 12-3 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 four students. For these four, 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 12-3, the error or residual sum of squares (SSE)is ________.