Question

Problem 3-26 The following data were collected during a study of consumer buying patterns: Observation 1 2 3 4 14 28 43 36 51 52 28 у 70 78 88 77 98 94 86 Observation 8 9 10 11 12 13 19 10 18 23 24 28 y 76 65 72 86 89 89 5 6 7 b. Obtain a linear regression line for the data (Round your intermediate calculations and final answers to 3 decimal places.) y= 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 = 49. (Round your intermediate calculations and final answers to 3 decimal places.) y=

Answer 1

Solution:

b: Regression Equation

c: R-Squared

The 66% of the variation in dependent variable y is explained by independent variable x.

d:

x = 49 , Hence,

summary:

|y X 70 14 SUMMARY OUTPUT 78 28 88 77 98 94 86 43 36 51 Regression Statistics Multiple R 0.812002 R Square 0.659347 Adjusted R Square 0.628379 Standard Error 6.034017 Observations 13 52 28 19 76 65 10 72 ANOVA 18 23 df 86 89 89 24 28 Regression Residual Total SS MS F ignificance F 1 775.1893 775.1893 21.29094 0.000747 11 400.503 36.40936 12 1175.692 Intercept Coefficientsandard Erri t Stat P-value Lower 95%Upper 95%ower 95.0%pper 95.0% 64.79124 4.118228 15.73279 6.89E-09 55.72708 73.8554 55.72708 73.8554 0.603513 0.130794 4.61421 0.000747 0.315636 0.89139 0.315636 0.89139 X