Exam 12: Simple Linear Regression

TABLE 12-2 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 six 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 12-2, to test whether a change in price will have any impact on sales, what would be the critical values? Use α = 0.05.

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

TABLE 12-8 It is believed that GPA (grade point average, based on a four-point scale) should have a positive linear relationship with ACT scores. Given below is the Microsoft Excel output for predicting GPA using ACT scores based a data set of eight randomly chosen students from a Big Ten university. -Referring to Table 12-8, the value of the measured (observed)test statistic of the F test for H₀: β₁ = 0 vs. H₁: β₁ = 0

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 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.

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 director of cooperative education wanted to test the hypothesis that the population slope was equal to 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 12-8 It is believed that GPA (grade point average, based on a four-point scale) should have a positive linear relationship with ACT scores. Given below is the Microsoft Excel output for predicting GPA using ACT scores based a data set of eight randomly chosen students from a Big Ten university. -Referring to Table 12-8, what are the decision and conclusion on testing whether there is any linear relationship at 1% level of significance between GPA and ACT scores?

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 director of cooperative education wanted to test the hypothesis that the population slope was equal to 0. The value of the test statistic is ________.

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, what percentage of the variation in composite score can be explained by the variation in spending per student?

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% confidence interval estimate for the mean sales made by brokers who have brought into the firm 24 new clients. The t critical value they would use is ________.

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

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. -You give a pre-employment examination to your applicants. The test is scored from 1 to 100. You have data on their sales at the end of one year measured in dollars. You want to know if there is any linear relationship between pre-employment examination score and sales. An appropriate test to use is the t test of the population correlation coefficient.

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 F test on whether the number of loan applications recorded affects the amount of time are ________.

TABLE 12-8 It is believed that GPA (grade point average, based on a four-point scale) should have a positive linear relationship with ACT scores. Given below is the Microsoft Excel output for predicting GPA using ACT scores based a data set of eight randomly chosen students from a Big Ten university. -Referring to Table 12-8, the value of the measured test statistic to test whether there is any linear relationship between GPA and ACT scores is _______.

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 coefficient of determination?

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 standard error of estimate is ________.

If the residuals in a regression analysis of time-ordered data are not correlated, the value of the Durbin-Watson D statistic should be near ________.

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 p-value of the measured t test statistic to test whether the number of loan applications recorded affects the amount of time 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 error or residual sum of squares (SSE)is ________.

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

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, 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.