Problem 3-26 The following data were collected during a study of consumer buying

Question

Problem 3-26 The following data were collected during a study of consumer buying patterns: Observation 20 27 43 78 84 79 y ObservationX 23 10 13 21 81 69 10 85 91 93 53 12 13 97 82 34 b. Obtain a linear regression line for the data.(Round your intermediate calculations and final answers to 3 decimal places.) 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.) % of the variation in the dependent variable is explained by the independent d. Use the equation determined in part b to predict the expected value of y for x47. (Round your intermediate calculations and final answers to 3 decimal places.) References eBook & Resources

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 66.141986 + 0.595646 x
Sample size: 13
R (correlation coefficient) = 0.78377658
R-sq = 0.61430572
Estimate of error standard deviation: 6.1057501

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

b) Regression equation:

y = 66.142 + 0.596 x

c) Percent of variation explained = R-sq = 0.61 = 61 %

d) For x = 47, y = 94.137

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 66.141986 4.470918 0 11 14.793827 <0.0001 Slope 0.595646 0.14230534 0 11 4.1856897 0.0015

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