Exam 13: Simple Linear Regression

The residuals represent

TABLE 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. Broker Cliente Sales 1 27 52 2 11 37 3 42 64 4 33 55 5 15 29 6 15 34 7 25 58 8 36 59 9 28 44 10 30 48 11 17 31 12 22 38 -Referring to Table 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. The p-value of the test is _______.

TABLE 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 Multiple R 0.142620229 R Square 0.02034053 Adjusted R Square -0.028642444 Standard Error 20.25979924 Observations 22 Coefficients Standard Enor T Stat p -value Intercept 39.39027309 37.24347659 1.057642216 0.302826622 Attendance 0.340583573 0.52852452 0.644404489 0.526635689 -Referring to Table 13-6, which of the following statements is true?

The confidence interval for the mean of Y is always narrower than the prediction interval for an individual response Y given the same data set, X value, and confidence level.

TABLE 13-10 The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousand of dollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the following results: Customers Sales (Thousands of Dollars) 907 11.20 926 11.05 713 8.21 741 9.21 780 9.42 898 10.08 510 6.73 529 7.02 460 6.12 872 9.52 650 7.53 603 7.25 -Referring to Table 13-10, the p-value of the t test and F test should be the same when testing whether the number of customers who make purchases is a good predictor for weekly sales.

TABLE 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. Student CoopJobs JobOffer 1 1 4 2 2 6 3 1 3 4 0 1 -Referring to Table 13-3, the director of cooperative education wanted to test the hypothesis that the true slope was equal to 0. The denominator of the test statistic is Sb1. The value of Sb1 in this sample is _______.

TABLE 13-10 The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousand of dollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the following results: Customers Sales (Thousands of Dollars) 907 11.20 926 11.05 713 8.21 741 9.21 780 9.42 898 10.08 510 6.73 529 7.02 460 6.12 872 9.52 650 7.53 603 7.25 -Referring to Table 13-3, the least squares estimate of the Y-intercept is_____ .

TABLE 13-10 The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousand of dollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the following results: Customers Sales (Thousands of Dollars) 907 11.20 926 11.05 713 8.21 741 9.21 780 9.42 898 10.08 510 6.73 529 7.02 460 6.12 872 9.52 650 7.53 603 7.25 -Referring to Table 13-10, the value of the t test statistic and F test statistic should be the same when testing whether the number of customers who make purchases is a good predictor for weekly sales.

TABLE 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's Data Analysis tool to analyze the last 4 years of quarterly data with the following results: Regression Statistics Multiple R 0.802 R Square 0.643 Adjusted R Square 0.618 Standard Error SYX 0.9224 Observations 16 ANOVA d f SS MS F Sig.F Regression 1 21.497 21.497 25.27 0.000 Error 14 11.912 0.851 Total 15 33.409 Predictor Coefficients Standard Error t Stat p -value Intercept 3.962 1.440 2.75 0.016 Industry 0.040451 0.008048 5.03 0.000 -Referring to Table 13-5, the coefficient of determination is ______.

TABLE 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. Student CoopJobs JobOffer 1 1 4 2 2 6 3 1 3 4 0 1 -Referring to Table 13-3, suppose the director of cooperative education wants to obtain a 95% confidence-interval estimate for the mean number of job offers received by people who have had exactly one cooperative education job. The t critical value she would use is_______

TABLE 13-10 The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousand of dollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the following results: Customers Sales (Thousands of Dollars) 907 11.20 926 11.05 713 8.21 741 9.21 780 9.42 898 10.08 510 6.73 529 7.02 460 6.12 872 9.52 650 7.53 603 7.25 -Referring to Table 13-10, what is the value of the F test statistic when testing whether the number of customers who make purchases is a good predictor for weekly sales?

TABLE 13-12 The manager of the purchasing department of a large banking organization would like to develop a model to predict the amount of time (measured in hours) it takes to process invoices. Data are collected from a sample of 30 days, and the number of invoices processed and completion time in hours is recorded. Below is the regression output: Regression Statistics Multiple R 0.9947 R Square 0.8924 Adjusted R Square 0.8886 Standard Error 0.3342 Observations 30 $\text { ANOVA }$ df SS MS F Significance F Regression 1 25.9438 25.9438 232.2200 4.3946-15 Residual 28 3.1282 0.1117 Total 29 29.072 Coeffcients StandardError t Stat p -value Lower 95\% Upper 95\% Invoices 0.4024 0.1236 3.2559 0.0030 0.1492 0.6555 Processed 0.0126 0.0008 15.2388 4.3946-15 0.0109 0.0143 -Referring to Table 13-12, the degrees of freedom for the F test on whether the number of invoices processed affects the amount of time are

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

TABLE 13-12 The manager of the purchasing department of a large banking organization would like to develop a model to predict the amount of time (measured in hours) it takes to process invoices. Data are collected from a sample of 30 days, and the number of invoices processed and completion time in hours is recorded. Below is the regression output: Regression Statistics Multiple R 0.9947 R Square 0.8924 Adjusted R Square 0.8886 Standard Error 0.3342 Observations 30 $\text{ANOVA}$ df SS M S F Significance F Regression 1 25.9438 25.9438 232.2200 4.3946-15 Residual 28 3.12820.1117 Total 29 29.072 -Referring to Table 13-12, the degrees of freedom for the t test on whether the number of invoices processed affects the amount of time are

TABLE 13-10 The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousand of dollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the following results: Customers Sales (Thousands of Dollars) 907 11.20 926 11.05 713 8.21 741 9.21 780 9.42 898 10.08 510 6.73 529 7.02 460 6.12 872 9.52 650 7.53 603 7.25 -Referring to Table 13-10, what are the values of the estimated intercept and slope?

TABLE 13-12 The manager of the purchasing department of a large banking organization would like to develop a model to predict the amount of time (measured in hours) it takes to process invoices. Data are collected from a sample of 30 days, and the number of invoices processed and completion time in hours is recorded. Below is the regression output: Regression Statistics Multiple R 0.9947 R Square 0.8924 Adjusted R Square 0.8886 Standard Error 0.3342 ations 30 d f SS MS F Significance F Regression 1 25.9438 25.9438 232.2200 4.3946-15 Residual 28 3.1282 0.1117 Total 29 29.072 Coefficients Standard Error t Stat p -value Lower 95\% Upper 95\% Invoices 0.4024 0.1236 3.2559 0.0030 0.1492 0.6555 Processed 0.0126 0.0008 15.2388 4.3946-15 0.0109 0.0143 -Referring to Table 13-12, there is sufficient evidence that the amount of time needed linearly depends on the number of invoices processed at a 1% level of significance.

If the Durbin-Watson statistic has a value close to 0, which assumption is violated?

TABLE 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. Student CoopJobs JobOffer 1 1 4 2 2 6 3 1 3 4 0 1 -Referring to Table 13-3, the coefficient of correlation is______ .

TABLE 13-12 The manager of the purchasing department of a large banking organization would like to develop a model to predict the amount of time (measured in hours) it takes to process invoices. Data are collected from a sample of 30 days, and the number of invoices processed and completion time in hours is recorded. Below is the regression output: Regression Statistics Multiple R 0.9947 R Square 0.8924 Adjusted R Square 0.8886 Standard Error 0.3342 ations 30 d f SS MS F Significance F Regression 1 25.9438 25.9438 232.2200 4.3946-15 Residual 28 3.1282 0.1117 Total 29 29.072 Coefficients Standard Error t Stat p -value Lower 95\% Upper 95\% Invoices 0.4024 0.1236 3.2559 0.0030 0.1492 0.6555 Processed 0.0126 0.0008 15.2388 4.3946-15 0.0109 0.0143 -Referring to Table 13-12, you can be 95% confident that the average amount of time needed to process one additional invoice is somewhere between 0.0109 and 0.0143 hours.

The Y-intercept (b₀) represents the