Exam 13: Simple Linear Regression

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 ________.

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% prediction interval for the number of job offers received by a student who has had exactly two cooperative education jobs.The prediction interval is from ________ to ________.

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, to test whether a change in price will have any impact on sales, what would be the critical values? Use = 0.05.

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 is the critical value for testing whether there is a linear relationship between revenue and the number of downloads at a 5% level of significance?

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% confidence interval estimate for the mean sales made by brokers who have brought into the firm 24 new clients.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 value of the measured t-test statistic to test whether composite score depends linearly on spending per student is ________.

The residual represents the discrepancy between the observed dependent variable and its _______ value.

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 assumptions appears to have been violated?

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.At a level of significance of 0.01, the null hypothesis should be _______ (rejected or not rejected).

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 degrees of freedom for the F test on whether HOURS affects SALARY are

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 p-value of the t test statistic when testing whether the number of customers who make a purchase affects weekly sales?

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 appropr iate null and alternative hypotheses are, respectively,

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

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 3.0.The p-value of the test is between ________ and ________.

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, which is the correct null hypothesis for testing whether the number of customers who make a purchase affects weekly sales?

A zero population correlation coefficient between a pair of random variables means that there is no linear relationship between the random variables.

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 Durbin-Watson statistic is inappropriate for this data set.

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 13-7 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 measured value of the test statistic is

If the correlation coefficient (r)= 1.00, then