Exam 12: Simple Linear Regression

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 interpretation of the coefficient of determination in this regression 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, what is the value of the standard error of the estimate?

TABLE 12-6 The following Microsoft 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 12-6, which of the following statements is true?

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, the null hypothesis for testing whether there is a linear relationship between revenue and the number of downloads is "There is no linear relationship between revenue and the number of downloads".

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 degrees of freedom for the F test on whether spending per student affects composite score are ________.

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 sufficient evidence that the amount of time needed linearly depends on the number of loan applications at a 1% level of significance.

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

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 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 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, set up a scatter plot.

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. 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 ________.

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 the estimated slope coefficient 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, 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 t critical value she would use is ________.