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 degrees of freedom for the F test on whether spending per student affects composite score are _________.

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 population slope was equal to 0.The value of the test statistic 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, the mean weekly sales will increase by an estimated $10 for each additional purchasing customer.

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, 93.98% of the total variation in weekly sales can be explained by the variation in the number of customers who make purchases.

SCENARIO 13-7 An investment specialist claims that if one holds a portfolio that moves in the opposite direction to the market index like the 500, then it is possible to reduce the variability of the portfolio's return.In other words, one can create a portfolio with positive returns but less exposure to risk. A sample of 26 years of S&P 500 i ndex and a portfolio consisting of stocks of private prisons, which are believed to be negatively related to the S&P 500 inde x, is collected.A regression analysis was performed by regressing the returns of the prison stocks portfolio (Y)on the returns of S&P 500 index ( X)to prove that the prison stocks portfolio is negatively related to the S&P 500 index at a 5% level of significance.The results are given in the following EXCEL output. -Referring to Scenario 13-7, to test whether the prison stocks portfolio is negatively related to the S&P 500 index, the p-value of the associated test statistic 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, what are the decision and conclusion on testing whether there is any linear relationship at 1% level of significance between GPA and ACT scores?

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 population slope was equal to 0.The denominator of the test statistic is .The value of in this sample 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 predicted sales will be

SCENARIO 13-7 An investment specialist claims that if one holds a portfolio that moves in the opposite direction to the market index like the 500, then it is possible to reduce the variability of the portfolio's return.In other words, one can create a portfolio with positive returns but less exposure to risk. A sample of 26 years of S&P 500 i ndex and a portfolio consisting of stocks of private prisons, which are believed to be negatively related to the S&P 500 inde x, is collected.A regression analysis was performed by regressing the returns of the prison stocks portfolio (Y)on the returns of S&P 500 index ( X)to prove that the prison stocks portfolio is negatively related to the S&P 500 index at a 5% level of significance.The results are given in the following EXCEL output. -Referring to Scenario 13-7, which of the following will be a correct conclusion?

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, 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?

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. -Referring to Scenario 13-6, which of the following statements is true?

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 13-5 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 prediction for a quarter in which X = 120 is Y = ________.

Based on the residual plot below, you will conclude that there might be a violation of which of the following assumptions.

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 ________.

In a simple linear regression problem, r and

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 ________.

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 Y-intercept 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 degrees of freedom of the t test statistic when testing whether the number of customers who make a purchase affects weekly sales?

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, ?