Exam 13: Simple Linear Regression

TABLE 13-6 The following Excel tables are obtained when "Score received on an exam (measured in percentage points)" (Y) is regressed on "percentage attendance" (X) for 22 students in a Statistics for Business and Economics course. -Referring to Table 13-6, which of the following statements is true?

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, the Durbin-Watson statistic is inappropriate for this data set.

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 value of the measured t test statistic to test whether composite score depends linearly on spending per student 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 degrees of freedom for the F test on whether spending per student affects composite score are ________.

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. The value of the 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, 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 ________.

Assuming a linear relationship between X and Y, if the coefficient of correlation (r) equals -0.30,

Referring to Table 13-2, if the price of the candy bar is set at $2, the predicted sales will be

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. For a test with a level of significance of 0.05, the null hypothesis should be rejected if the value of the test statistic 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 standard error of estimate 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: Note: 4.3946E-15 is 4.3946 × -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 13-10 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 values of the estimated intercept and slope?

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% prediction interval for the weekly sales of a store that has 600 purchasing customers.

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 estimate of σ, the standard deviation of the random error term (standard error of the estimate) in the model.

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. -Referring to Table 13-9, the error sum of squares (SSE) of the above regression is

The value of r is always positive.

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 t test statistic when testing whether the number of customers who make a purchase affects weekly sales?

If the Durbin-Watson statistic has a value close to 0, which assumption is violated?

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, the error sum of squares (SSE) 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, set up a scatter plot.