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 p-value of the measured F-test statistic to test whether the number of loan applications recorded affects the amount of time is .

The slope (b₁)represents

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

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 invoices processed,the p-value of the test statistic is .

SCENARIO 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 Scenario 13-2,what is the standard error of the regression slope estimate,} S_b1 ^?

The least squares method minimizes which of the following?

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 13-11,what is the p-value for testing whether there is a linear relationship between revenue and the number of downloads 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,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 .

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. Note: 2.051 E - 05 = 2.051*1^0-5 and 5.944 E -18 = 5.944 *10 ^-18 . -Referring to Scenario 13-8,the value of the measured test statistic to test whether there is any linear relationship between GPA and ACT is

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,there is no evidence of positive autocorrelation if the Durbin-Watson test statistic is found to be 1.78.

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 estimates of the Y-intercept and slope are _____ and _____ ,respectively.

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,suppose the managers of the brokerage firm want to construct n a 99% prediction interval for the sales made by a broker who has brought into the firm 18 new clients.The t critical value they would use is .

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 13-11,the homoscedasticity of error assumption appears to have been violated.

SCENARIO 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: Y_i = $\beta$ ₀ + $\beta$ ₁ X_i + $\varepsilon$ _i The results of the simple linear regression are provided below. ? = -2,700 +20 X ,S_YX = 65,two-tail p value = 0.034 (for testing $\beta$ ₁) 11eb129a_22de_eb6b_935a_932306595b21_TB6723_00 -Referring to Scenario 13-1,interpret the estimate of $\beta$ ₀ ,the Y-intercept of the line.

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 value of the F test statistic equals the square of the t test statistic when testing whether the number of customers who make purchases is a good predictor for weekly sales.

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 : $\rho$ $\gt$ 0 against the one-sided alternative H₁ : $\pm$$\gt$ 0.To test H₀ : $\pm$ = 0 against the two-sided alternative H₁ : $\rho$ $\neq$ 0 at a significance level of 0.1,the p-value 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 coefficient of determination is .

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

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 90% confidence interval for the mean change in the amount of time needed as a result of recording one additional loan application 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,_____ % of the total variation in sales generated can be explained by the number of new clients brought in.