Exam 13: Simple Linear Regression

SCENARIO 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 Scenario 13-12, the degrees of freedom for the t test on whether the number of loan applications recorded affects the amount of time are

SCENARIO 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 Scenario 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.

SCENARIO 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 Scenario 13-11, there is sufficient evidence that revenue and the number of downloads are linearly related at a 5% level of significance.

SCENARIO 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 Scenario 13-3, 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 ________.

SCENARIO 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 Scenario 13-13, 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 .

SCENARIO 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 Scenario 13-12, to test the claim that the mean amount of time depends positively on the number of loan applications recorded against the null hypothesis that the mean amount of time does not depend linearly on the number of loan applications processed, the p-value of the test statistic is ____.

SCENARIO 13-5 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 4 years of quarterly data with the following results: -Referring to Scenario 13-5, the standard error of the estimate is ________.

The confidence interval for the mean of Y is always narrower than the prediction interval for an individual response Y given the same data set, X value, and confidence level.

SCENARIO 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. -Regression analysis is used for prediction, while correlation analysis is used to measure the strength of the association between two numerical variables.

SCENARIO 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 Scenario 13-13, the regression mean square (MSR)of the above regression is _____.

SCENARIO 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 Scenario 13-11, which of the following is the correct alternative hypothesis for testing whether there is a linear relationship between revenue and the number of downloads?

SCENARIO 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 Scenario 13-3, the least squares estimate of the slope is __________.

SCENARIO 13-8 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 Excel output for predicting GPA using ACT scores based a data set of 8 randomly chosen students from a Big-Ten university. -Referring to Scenario 13-8, the value of the measured (observed)test statistic of the F-test for

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 __________.

SCENARIO 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 Scenario 13-4, the prediction for the amount of sales (in $1,000s)for a person who brings 25 new clients into the firm is ________.

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

SCENARIO 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 Scenario 13-4, set up a scatter plot.

SCENARIO 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 Scenario 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?

SCENARIO 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 Scenario 13-10, it is inappropriate to compute the Durbin- Watson statistic and test for autocorrelation in this case.

SCENARIO 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 Scenario 13-10, the null hypothesis for testing whether the number of customers who make a purchase effects weekly sales cannot be rejected if a 1% probability of committing a type I error is desired.