ECON 2330 Assignment#3 - Group (Check Moodle for your Group) Winter 2019

Note: Once you completed these questions using the built-in process under Data Analysis in Excel or Minitab to support your results, you need to save the outputs of Excel or Minitab as a picture and add it to your solutions in MS Word for each part of these Problems, save all solutions as one PDF file and upload it in Moodle. Otherwise, only partial mark will be given.

Problem#1 Parts (a). (c), and (d) of this Problem must be done in Minitab, only solutions by Minitab will be given full mark.

To help consumers in purchasing a laptop computer, Consumer Reports calculates an overall test score for each computer tested based upon rating factors such as ergonomics, portability, performance, display, and battery life. Higher overall scores indicate better test results. The following data show the average retail price and the overall score for ten 13-inch models (Consumer Reports website, October 25, 2012).

Brand & Model Price ($) Overall Score

Samsung Ultrabook NP900X3C-A01US 1250 83 Apple MacBook Air MC965LL/A 1300 83 Apple MacBook Air MD231LL/A 1200 82 HP ENVY 13-2050nr Spectre XT 950 79 Sony VAIO SVS13112FXB 800 77 Acer Aspire S5-391-9880 Ultrabook 1200 74 Apple MacBook Pro MD101LL/A 1200 74 Apple MacBook Pro MD313LL/A 1000 73 Dell Inspiron I13Z-6591SLV 700 67 Samsung NP535U3C-A01US 600 63

a) Develop a scatter diagram with price as the independent variable.b) What does the scatter diagram developed in part (a) indicate about the relationship

between the two variables?c) Use the Least Squares method to develop the estimated regression equation.d) Provide an interpretation of the slope of the estimated regression equation.e) Another laptop that Consumer Reports tested is the Acer Aspire S3-951-6646 Ultrabook;

the price for this laptop was $700. Predict the overall score for this laptop using theestimated regression equation developed in part (c).

Problem#2 All parts of this Problem must be done in Excel, only solutions by Excel will be given full mark.

The Dow Jones Industrial Average (DJIA) and the Standard & Poor’s 500 (S&P 500) indexes are used as measures of overall movement in the stock market. The DJIA is based on the price movements of 30 large companies; the S&P 500 is an index composed of 500 stocks. Some say the S&P 500 is a better measure of stock market performance because it is broader based. The closing price for the DJIA and the S&P 500 for 15 weeks, beginning with January 6, 2012, follow (Barron’s website, April 17, 2012).

Date DJIA S&P January 6 12360 1278 January 13 12422 1289 January 20 12720 1315 January 27 12660 1316 February 3 12862 1345 February 10 12801 1343 February 17 12950 1362 February 24 12983 1366 March 2 12978 1370 March 9 12922 1371 March 16 13233 1404 March 23 13081 1397 March 30 13212 1408 April 5 13060 1398 April 13 12850 1370

a) Develop a scatter diagram with DJIA as the independent variable. b) Develop the estimated regression equation. c) Test for a significant relationship. Use α=0.05. d) Did the estimated regression equation provide a good fit? Explain. e) Suppose that the closing price for the DJIA is 13,500. Predict the closing price for the

S&P 500. f) Should we be concerned that the DJIA value of 13,500 used to predict the S&P 500 value

in part(e) is beyond the range of the data used to develop the estimated regression equation?

Problem #3 All parts of this Problem must be done in Minitab, only solutions by Minitab will be given full mark.

PC Magazine provided ratings for several characteristics of computer monitors, including an overall rating (PC Magazine website, April, 2015). The following data show the rating for contrast ratio, resolution, and the overall rating for ten monitors tested using a 0–100 point scale. The highest rated monitor was the BenQ BL3201PH, with an overall rating of 87.

Model Contrast Ratio

Resolution Overall Rating

BenQ BL3201PH 78 89 87 AOC U2868PQU 98 87 86 NEC MultiSync PA322UHD 84 82 85 Acer XB280HK 78 77 82 Asus ROG Swift PG278Q 65 82 82 AOC E1759Fwu 57 78 82 Dell UltraSharp UZ2715H 56 83 81 NEC MultiSync EA244UHD 77 75 79 HP DreamColor Z27x 47 81 77 Dell UltraSharp UZ2315H 55 70 76

a) Develop the estimated regression equation that can be used to predict the Overall Rating using the Contrast Ratio Rating.

b) Develop the estimated regression equation that can be used to predict the Overall Rating using both the Contrast Ratio Rating and the Resolution Rating.

c) Predict the overall Overall Rating for a computer monitor computer that has a Contrast Ratio Rating of 85 and a Resolution Rating of 74.

Problem #4 All parts of this Problem must be done in Minitab and/or Excel.

The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains (Consumer Reports website, February 11, 2009). Assume the following data are representative of the results reported. The variable type indicates whether the restaurant is an Italian restaurant or a seafood/steakhouse. Price indicates the average amount paid per person for dinner and drinks, minus the tip. Score reflects diners’ overall satisfaction, with higher values indicating greater overall satisfaction. A score of 80 can be interpreted as very satisfied.

Restaurant Type Price ($) Score Bertucci's Italian 16 77 Black Angus Steakhouse Seafood/Steakhouse 24 79 Bonefish Grill Seafood/Steakhouse 26 85 Bravo! Cucina Italiana Italian 18 84 Buca di Beppo Italian 17 81 Bugaboo Creek Steak House Seafood/Steakhouse 18 77 Carrabba's Italian Grill Italian 23 86 Charlie Brown's Steakhouse Seafood/Steakhouse 17 75 Il Fornaio Italian 28 83 Joe's Crab Shack Seafood/Steakhouse 15 71 Johnny Carino's Italian Italian 17 81 Lone Star Steakhouse & Saloon Seafood/Steakhouse 17 76 LongHorn Steakhouse Seafood/Steakhouse 19 81 Maggiano's Little Italy Italian 22 83 McGrath's Fish House Seafood/Steakhouse 16 81 Olive Garden Italian 19 81 Outback Steakhouse Seafood/Steakhouse 20 80 Red Lobster Seafood/Steakhouse 18 78 Romano's Macaroni Grill Italian 18 82 The Old Spaghetti Factory Italian 12 79 Uno Chicago Grill Italian 16 76

a) Develop the estimated regression equation to show how overall customer satisfaction isrelated to the independent variable average meal price.

b) At the 0.05 level of significance, test whether the estimated regression equationdeveloped in part (a) indicates a significant relationship between overall customersatisfaction and average meal price.

c) Develop a dummy variable that will account for the type of restaurant (Italian orseafood/steakhouse).

d) Develop the estimated regression equation to show how overall customer satisfaction isrelated to the average meal price and the type of restaurant.

e) Is type of restaurant a significant factor in overall customer satisfaction?f) Predict the Consumer Reports customer satisfaction score for a seafood/steakhouse that

has an average meal price of $20. How much would the predicted score have changed foran Italian restaurant?

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Problem#5 All parts of this Problem must be done in Minitab and/or Excel.

Over the past few years the percentage of students who leave Lakeland College at the end of the first year has increased. Last year Lakeland started a voluntary one-week orientation program to help first-year students adjust to campus life. If Lakeland is able to show that the orientation program has a positive effect on retention, they will consider making the program a requirement for all first-year students. Lakeland’s administration also suspects that students with lower GPAs have a higher probability of leaving Lakeland at the end of the first year. In order to investigate the relation of these variables to retention, Lakeland selected a random sample of 100 students from last year’s entering class. The data are contained in the data set named Lakeland. The dependent variable was coded as y=1 if the student returned to Lakeland for the sophomore year and y=0 if not. The two independent variables are:

a) Write the logistic regression equation relating X1 and to X2 .b) What is the interpretation of E (y ) when X2=0?c) Use both independent variables and Minitab to compute the estimated logit.d) Conduct a test for overall significance using Use α=0.05.e) Use α=0.05 to determine whether each of the independent variables is significant.f) Use the estimated logit computed in part (c) to estimate the probability that students with a 2.5

grade point average who did not attend the orientation program will return to Lakeland for theirsophomore year. What is the estimated probability for students with a 2.5 grade point average whoattended the orientation program?

g) What is the estimated odds ratio for the orientation program? Interpret it.h) Would you recommend making the orientation program a required activity? Why or why not?

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All parts of this Problem must be done in Excel.

Problem#6: The Transactional Records Access Clearinghouse at Syracuse University reported data showing the chance of an Internal Revenue Service (IRS) audit. The data in file IRSAudit show the average adjusted gross income reported (in $ thousands) and the percent of the returns that were audited for 20 selected IRS districts.

a. Use EXCEL to create a scatterplot with average adjusted gross income reported on thehorizontal axis and percent of the returns that were audited on the vertical axis. Includethe fitted simple linear regression line on the plot and include the plot in your answer.What does the scatterplot indicate about the relationship between the average adjustedgross income reported and the percent of the returns that were audited?

b. Use EXCEL to estimate a simple linear regression model using least squares. Report theestimated regression equation that could be used to predict the percent audited given theaverage adjusted gross income reported.

c. Is there a significant linear relationship between the two variables based on asignificance level 𝛼𝛼 = 0.05?

d. Use the estimated regression equation to predict the percent audited for a district with anaverage adjusted gross income of $35,000.

e. Use EXCEL to compute a 95% confidence interval for the average percent audited ofdistricts with an average adjusted gross income of $35,000. Interpret the interval in thecontext of the application.

f. Use EXCEL to compute a 95% prediction interval for the percent audited of an individualdistrict with an average adjusted gross income of $35,000. Interpret the interval in thecontext of the application.

g. Use the regression output in EXCEL to calculate the coefficient of determination, 𝑟𝑟 2from the sum of squares due to regression (SSR) and the total sum of squares (SST).Interpret your calculated value of 𝑟𝑟 2 in the context of the application.

h. The following plots were created from the estimated simple linear regression model fitto this dataset.

We can characterize the left-hand plot as a random cloud of points in a rough horizontal band and the right-hand plot as points that lie reasonably close to the 45° line. Briefly describe what this tells us about the simple linear regression model assumptions in this case.

i. The largest absolute standardized residual for this simple linear regression analysis is1.703, while the highest leverage is 0.237. Briefly describe what this tells us aboutpotentially influential observations in this analysis. An auditor notes that the coefficientof determination is relatively low for this analysis and hence the least squares line doesnot provide a very good fit and the model has little value. Do you agree with thisassessment? Why or why not?

All parts of this Problem must be done in Excel. Problem#7: A factorial experiment was designed to test for any significant differences in the time needed to perform English to foreign language translations with two computerized language translator systems. Because the type of language translated was also considered an important factor, translations were made with both systems for three different languages: Spanish, French, and German. The data for translation time in hours are contained in the file Translations. Use a significance level 𝛼𝛼 = 0.05 to test for differences due to language translator system, type of language, and interaction.

a. Use EXCEL to compute the p-values for system, language, and the interaction.

b. What are your hypothesis test decisions for each of system, language, and theinteraction?

c. What are your conclusions in the context of the application? Your conclusions shouldrelate back to the question.

Pred(Percent Audited) / Standardized residuals Q-Q plot (Std. residual)

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Parts 4, 5, 6 of this Problem must be done in Excel. Problem # 8 Suppose that a local chapter of sales professionals conducted a survey of its membership to study the relationship, if any, between the years of experience and salary for individuals employed in inside and outside sales positions. On the survey, respondents were asked to specify one of three levels of years of experience: low (1–10 years), medium (11–20 years), and high (21 or more years). A portion of the data obtained follow. The complete data set, consisting of 120 observations, is contained in the file named SalesSalary.

1. Use descriptive statistics to summarize the data.2. Develop a 95% confidence interval estimate of the mean annual salary

for all salespersons, regardless of years of experience and type ofposition.

3. Develop a 95% confidence interval estimate of the mean salary foroutside salespersons.

4. Use analysis of variance to test for any significant differences due toposition. Use a 0.05 level of significance, and for now, ignore theeffect of years of experience.

5. Use analysis of variance to test for any significant differences due toyears of experience. Use a .05 level of significance, and for now,ignore the effect of position.

6. At the 0.05 level of significance test for any significant differencesdue to position, years of experience, and interaction.

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