Exam 13: Simple Linear Regression

The Regression Sum of Squares (SSR)can never be greater than the Total Sum of Squares (SST).

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,a 95% confidence interval for $\beta$ ₁ is (15,30).Interpret the interval.

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 13-4 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.For a test with a level of significance of 0.01,the null hypothesis should be rejected if the value of the test statistic is .

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

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 S&P 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 index and a portfolio consisting of stocks of private prisons,which are believed to be negatively related to the S&P 500 index,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 13-3 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 prediction for the number of job offers for a person with 2 coop jobs is .

If the plot of the residuals is fan shaped,which assumption is 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 regression sum of squares (SSR)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 degrees of freedom for the t test on whether the number of loan applications recorded affects the amount of time are

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,there appears to be autocorrelation in the residuals.

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 error or residual sum of squares (SSE)is .

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 13-8,what are the decision and conclusion on testing whether there is any linear relationship at 1% level of significance between GPA and ACT scores?

Testing for the existence of correlation is equivalent 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,what is the estimated mean change in the sales of the candy bar if price goes up by $1.00?

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,to test the claim that SALARY depends positively on HOURS against the null hypothesis that SALARY does not depend linearly on HOURS,the p-value of the test statistic 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 model appears to be adequate based on the residual analyses.

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,the normality of error assumption appears to have been violated.

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,if the state decides to spend 1,000 dollar more per student,the estimated change in mean composite score 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,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 decision that should be made implies that _____ (there is a or there is no)linear dependent relationship between the independent and dependent variables.