Exam 13: Simple Linear Regression

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 estimated slope coefficient is .

In a simple linear regression the best fitting linear model always passes through point (x̅,y̅).

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.

Data that exhibit an autocorrelation effect violate the regression assumption of independence.

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 estimated slope for the candy bar price and sales data?

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,if the price of the candy bar is set at $2,the predicted sales will be

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 conclusion on the test of whether composite score depends linearly on spending per student using a 10% level of significance 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,suppose the managers of the brokerage firm want to construct a 99% prediction interval for the sales made by a broker who has brought into the firm 18 new clients.The prediction interval is from _____ to _____ .

The Durbin-Watson D statistic is used to check the assumption of normality.

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 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 null hypothesis should be _____ (rejected or not rejected).

The standard error of the estimate is a measure of

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,what are the critical values of the Durbin-Watson test statistic using the 5% level of significance to test for evidence of positive autocorrelation?

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 p-value of the test is between _____ and _____.

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.

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 coefficient of determination is .

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 coefficient of determination?

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 total sum of squares (SST)is .

The width of the prediction interval for the predicted value of Y is dependent on

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 ?,the standard deviation of the random error term (standard error of the estimate)in the model.

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 do the lower and upper limits of the 95% confidence interval estimate for the mean change in revenue as a result of a one thousand increase in the number of downloads?