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Unformatted text preview: ISDS Homework 10 Solutions. Linear Regression &amp; Correlation Panayiotis Skordi 1. The following sample observations were randomly selected. X: 5 3 6 3 4 4 6 8 Y: 13 15 7 12 13 11 9 5 a. Determine the coefficient of correlation. b. Determine the coefficient of determination. c. Interpret the result. a. [ ][ ] ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 2 85 983 8 39 211 8 85 39 378 8 ) ( ) ( ) ( ) ( ) ( = = y y n x x n y x xy n r ( 29 ( 29 ( 29 ( 29 89 . 639 167 291 7225 7864 1521 1688 3315 3024 = = = The  0.89 indicates a very strong negative relationship between X and Y . b. The coefficient of determination is 0.7921, found by ( 0.89) 2 . c. X accounts for 79 percent of the variation in Y . 1 X Y XY 2 X 2 Y 5 1 3 65 25 169 3 1 5 45 9 225 6 7 42 36 49 3 1 2 36 9 144 4 1 3 52 16 169 4 1 1 44 16 121 6 9 54 36 81 2. Bilo Appliance Stores has outlets in several large metropolitan areas in New England. The general sales manager plans to air a commercial for a digital camera on selected local TV stations prior to a sale starting on Saturday and ending Sunday. She plans to get the information for SaturdaySunday digital camera sales at the outlets and pair them with the number of times the advertisement was shown on the local TV stations. The purpose is to find whether there is any relationship between the number of times the advertisement was aired and digital camera sales. The pairings are: Location of Number of SaturdaySunday Sales TV Station Airings ($ thousands) Providence 4 15 Springfield 2 8 New Haven 5 21 Boston 6 24 Hartford 3 17 a. What is the dependent variable? b. Draw a scatter diagram. c. Determine the coefficient of correlation. d. Determine the coefficient of determination. e. Interpret these statistical measures. a. Sales b. 2 10 20 30 2 3 4 5 6 Number of Advertisements Sales($000) [ ][ ] ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 2 85 595 , 1 5 20 90 5 85 20 376 5 ) ( ) ( ) ( ) ( ) ( = = y y n x x n y x xy n r ( 29 ( 29 ( 29 93 . 750 50 180 225 , 7 975 , 7 400 450 700 , 1 880 , 1 = = = d. The coefficient of determination is 0.8649, found by (0.93) 2 e. There is a strong positive association between the variables. The number of airings explains about 86 percent of the variation in sales. X Y XY 2 X 2 Y 4 1 5 60 16 225 2 8 16 4 64 5 2 1 10 5 25 441 6 2 4 14 4 36 576 3 1 7 51 9 289 2 8 5 37 6 90 1,595 3 3. The owner of Maumee FordMercury wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year....
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 Fall '07
 Skordi
 Correlation and dependence, Pearson productmoment correlation coefficient, xy, Spearman's rank correlation coefficient, scatter diagram.

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