Exam 13: Simple Linear Regression

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

The coefficient of determination (r²)tells you

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 t critical value she would use is .

The sample correlation coefficient between X and Y is 0.375.It has been found out that the p- value is 0.744 when testing H₀ : $\rho$ = 0 against the one-sided alternative H₁: $\rho$ $\lt$ 0.To test H₀ : $\rho$ = 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 partner wants to test for autocorrelation using the Durbin-Watson statistic.Using a level of significance of 0.05,the decision he should make is:

If the correlation coefficient (r)= 1.00,then

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 prediction for the amount of sales (in $1,000s)for a person who brings 25 new clients into the firm 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 13-10,93.98% of the total variation in weekly sales can be explained by the variation in the number of customers who make purchases.

SCENARIO 13-3 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 13-9 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 13-9,the error sum of squares (SSE)of the above regression 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.

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 alternative hypothesis for testing whether there is a linear relationship between revenue and the number of downloads?

The Chancellor of a university has commissioned a team to collect data on students' GPAs and the amount of time they spend bar hopping every week (measured in minutes).He wants to know if imposing much tougher regulations on all campus bars to make it more difficult for students to spend time in any campus bar will have a significant impact on general students' GPAs.His team should use a t test on the slope of the population 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 value of the measured t-test statistic to test whether composite score depends linearly on spending per student is .

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,what percentage of the variation in composite score can be explained by the variation in spending per student?

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 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 13-12,the estimated mean amount of time it takes to record 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,suppose the managers of the brokerage firm want to construct both a 99% confidence interval estimate and a 99% prediction interval for X = 24.The confidence interval estimate would be the (wider or narrower)of the two intervals.

If the correlation coefficient (r)= 1.00,then

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 null hypothesis for testing whether the number of customers who make a purchase effects weekly sales cannot be rejected if a 1% probability of committing a type I error is desired.