Question

The following data were collected during a study of consumer buying patterns: Observation 1 2 3 4 5 6 7 12 21 44 29 49 46 29 у 78 76 83 81 93 99 85 Observation 8 9 10 11 12 13 13 18 19 17 25 30 у 77 70 69 84 87 86 b. Obtain a linear regression line for the data.(Round your intermediate calculations and final answers to 3 decimal places.) y= + х c. What percentage of the variation is explained by the regression line? (Do not round intermediate calculations. Round your answer to the nearest whole percent. Omit the "%" sign in your response.) Approximately % of the variation in the dependent variable is explained by the independent variable. d. Use the equation determined in part b to predict the expected value of y for x = 41. (Round your intermediate calculations and final answers to 3 decimal places.) y=1

Answer 1

Based on the above data, we find the equation of the line and $r^{2}$ as shown below:

X Observation 1 2 12 y 78 76 83 21 44 120 3 4 29 81 5 49 93 100 y = 0.5094x + 68.362 R? = 0.563 46 99 . 6 7 8 29 85 . . 80 13 77 9 18 70 . 10 19 69 60 11 17 84 12 25 87 13 86 40 30 352 TOTAL 1068 20 0 0 10 20 30 40 50 60

As seen from above,

y = 68.362 + 0.5094x

c) $r^{2}$ = 0.563

r = 0.7503

Hence, approx 75% of the variation in the dependent variable is explained by the independent variable

d) For x = 41,

y = 68.362 + 0.5094*41 = 89.2474 = 89.247

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