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Exam 13: Simple Linear Regression

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Question 21

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The Y-intercept (b₀) represents the

A) estimated average Y when X = 0.
B) change in estimated average Y per unit change in X.
C) predicted value of Y.
D) variation around the sample regression line.

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Question 22

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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 critical value at 5% level of significance of the F test on whether spending per student affects composite score is ________.

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Question 23

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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 decision that should be made implies that the number of new clients brought in ________ ('had' or 'did not have')a positive impact on the amount of sales generated.

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

Testing for the existence of correlation is equivalent to

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

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: -True or False: Referring to Table 13-12,you can be 95% confident that the mean amount of time needed to record one additional loan application is somewhere between 0.0109 and 0.0143 hours.

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,generate the scatter plot.

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: -True or False: Referring to Table 13-10,the mean weekly sales will increase by an estimated $0.01 for each additional purchasing customer.

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: -Referring to Table 13-12,the estimated mean amount of time it takes to record one additional loan application is

TABLE 13-2 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 6 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: -The residual represents the discrepancy between the observed dependent variable and its ________ value.

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. -True or False: 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 students 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 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.At a level of significance of 0.01,the decision that should be made implies that ________ ('there is a' or 'there is no')linear dependent relationship between the independent and dependent variables.

If the correlation coefficient (r) = 1.00,then

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

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 estimated change in mean salary (in thousands of dollars) as a result of spending an extra hour per day studying is

True or False: Data that exhibit an autocorrelation effect violate the regression assumption of independence.

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,set up a scatter plot.

TABLE 13-2 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 6 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 13-2,to test that the regression coefficient,β₁,is not equal to 0,what would be the critical values? Use α = 0.05.

The residuals represent