## (solution) Grand Canyon BUSINESS 352 Fitting a straight line to a set of data yields the following prediction line

Fitting a straight line to a set of data yields the following prediction line: Yn i = 16 - 0.5Xi a. Interpret the meaning of the Y intercept, b0. b. Interpret the meaning of the slope, b1. c. Predict the value of Y for X = 6. When performing a x2 test of independence in a contingency table with r rows and c columns, determine the upper-tail critical value of the test statistic in each of the following circumstances: a. a = 0.05, r = 4 rows, c = 5 columns b. a = 0.01, r = 4 rows, c = 5 columns c. a = 0.01, r = 4 rows, c = 6 columns d. a = 0.01, r = 3 rows, c = 6 columns e. a = 0.01, r = 6 rows, c = 3 columns An agent for a residential real estate company in a suburb located outside of Washington, DC, has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward that goal, the agent would like to use the size of an apartment, as defined by square footage to predict the monthly rental cost. The agent selects a sample of 48 one-bedroom apartments and collects and stores the data in RentSilverSpring . a. Construct a scatter plot. b. Use the least-squares method to determine the regression coefficients b0 and b1. c. Interpret the meaning of b0 and b1 in this problem. d. Predict the mean monthly rent for an apartment that has 800 square feet. e. Why would it not be appropriate to use the model to predict the monthly rent for apartments that have 1,500 square feet? f. Your friends Jim and Jennifer are considering signing a lease for a one-bedroom apartment in this residential neighborhood. They are trying to decide between two apartments, one with 800 square feet for a monthly rent of \$1,130 and the other with 830 square feet for a monthly rent of \$1,410. Based on Size (Square ent (\$) R 524 1110 616 1175 666 1190 830 1410 450 1210 550 1225 780 1480 815 1490 1070 1495 610 1680 835 1810 660 1625 590 1469 675 1395 744 1150 820 1140 912 1220 628 1434 645 1519 840 1105 800 1130 804 1250 950 1449 800 1168 787 1224 960 1391 750 1145 690 1093 840 1353 850 1530 965 1650 1060 1740 665 1235 775 1550 960 1545 827 1583 655 1575 535 1310 625 1195 749 1200 634 1185 641 1444 860 1385 740 1275 593 1050 880 1650 895 1340 692 1560 Starbucks Coffee Co. uses a data-based approach to improving the quality and customer satisfaction of its products. When survey data indicated that Starbucks needed to improve its package-sealing process, an experiment was conducted to determine the factors in the bag-sealing equipment that might be affecting the ease of opening the bag without tearing the inner liner of the bag. (Data extracted from L. Johnson and S. Burrows, “For Starbucks, It’s in the Bag,” Quality Progress, March 2011, pp. 17–23.) One factor that could affect the rating of the ability of the bag to resist tears was the plate gap on the bag-sealing equipment. Data were collected on 19 bags in which the plate gap was varied. The results are stored in Starbucks . a. Construct a scatter plot. b. Assuming a linear relationship, use the least-squares method to determine the regression coefficients b0 and b1. c. Interpret the meaning of the slope, b1, in this problem. d. Predict the mean tear rating when the plate gap is equal to 0. e. What should you tell management of Starbucks about the relationship between the plate gap and the tear rating? Tear Viscosity Pressure Plate Gap 0.00 350.00 180.00 0.00 0.00 350.00 170.00 0.00 0.45 319.00 186.00 1.80 0.85 380.00 174.00 1.80 0.35 350.00 180.00 0.00 0.30 300.00 180.00 0.00 0.70 400.00 180.00 0.00 1.90 350.00 190.00 0.00 0.25 350.00 180.00 0.00 0.10 319.00 186.00 -1.80 0.15 380.00 186.00 -1.80 3.90 350.00 180.00 3.00 0.00 380.00 174.00 -1.80 0.55 350.00 180.00 0.00 0.00 350.00 180.00 -3.00 0.05 319.00 174.00 -1.80 0.40 319.00 174.00 1.80 4.30 380.00 186.00 1.80 0.00 350.00 180.00 0.00 In Problem 12.7 on page 424, you used the plate gap on the bag-sealing equipment to predict the tear rating of a bag of coffee (stored in Starbucks ). Using the results of that problem, a. determine the coefficient of determination, r2, and interpret its meaning. b. determine the standard error of the estimate. c. How useful do you think this regression model is for predicting the tear rating based on the plate gap in the bag-sealing equipment? In Problem 12.9 on page 424, an agent for a real estate company wanted to predict the monthly rent for onebedroom apartments, based on the size of the apartment (stored in Rent-SilverSpring ). Using the results of that problem, a. determine the coefficient of determination, r2, and interpret its meaning. b. determine the standard error of the estimate. c. How useful do you think this regression model is for predicting the monthly rent? d. Can you think of other variables that might explain the variation in monthly rent?

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