Exam 13: Simple Linear Regression

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,the interpretation of the coefficient of determination in this regression 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 tha the population slope was equal to 0.The denominator of the test statistic is s_b1 .The value of _b1 in this sample 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,the error sum of squares (SSE)of the above regression 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 13-4 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 standard error of estimate 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 standard error of the estimated slope coefficient 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,the decision on the test of whether composite score depends linearly on spending per student using a 10% level of significance is to _____ (reject or not reject)^H₀.

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 13-10 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,it is inappropriate to compute the Durbin-Watson statistic and test for autocorrelation in this case.

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 critical values of the test are d_L =_____ ,and d_U =_____ .

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.

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,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 13-12 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 sufficient evidence that the amount of time needed linearly depends on the number of loan applications at a 1% level of significance.

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,interpret the p-value for testing whether $\beta$ ₁ 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 13-11,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?

What do we mean when we say that a simple linear regression model is "statistically" useful?

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 is the standard deviation of the composite score around the regression line?

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 coefficient of correlation 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 mean weekly sales when the number of customers who make purchases is 600.

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 F test statistic when testing whether the number of customers who make purchases is a good predictor for weekly sales?