Exam 13: Simple Linear Regression

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 p-value of the measured t-test statistic to test whether composite score depends linearly on spending per student 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.

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 denominator of the test statistic is .The value of in this sample 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, construct a 95% confidence interval for the change in mean weekly sales when the number of customers who make purchases increases by one.

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 against the one-sided alternative .To test against the two-sided alternative at a significance level of 0.1, the p-value 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 are the values of the estimated intercept and slope?

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: The results of the simple linear regression are provided below. two-tail p value =0.034 (for testing -Referring to Scenario 13-1, interpret the p-value for testing whether exceeds 0.

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 F test on whether the number of load applications recorded affects the amount of time are

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 13-8 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, what is the predicted value of GPA when ACT = 20?

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 least squares estimate of the slope 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, the estimated mean amount of time it takes to record one additional loan application is

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 against the two-sided alternative To test against the one-sided alternative at a significance level of 0.1, the p-value 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, the null hypothesis that there is no linear relationship between revenue and the number of downloads should be rejected at a 5% level of significance.

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 correlation coefficient is ________.

The Y-intercept represents the

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 a 95% probability that the mean amount of time needed to record one additional loan application is somewhere between 0.0109 and 0.0143 hours.

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 against the two-sided alternative To test against the one-sided alternative at a significance level of 0.1, the p-value 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, if the price of the candy bar is set at $2, the estimated mean sales will be