Show all work, calculations, and formulas and be sure to include all the calcula
ID: 3232080 • Letter: S
Question
Show all work, calculations, and formulas and be sure to include all the calculations/steps needed to calculate the means, standard deviations, correlation coefficient, slope, y-intercept, and the coefficient of determination. Round to three decimal places.
2. In a recent study, economists from Pennsylvania State University performed a simple linear regression model using the least squares principle to determine if there was a relationship between annual taxes and the average price of a home. Their results are compiled below.
Predictor
Coefficient
SE of Coefficient
t
Intercept
326072.15
49.95
4.24
Tax
1.09107
0.05872
18.58
ANOVA
Source of Variation
SS
DF
MS
F
Regression
11984585
1
11984585
345.24
Error
3644994
105
34714
Total
15629579
106
a. Determine the regression equation.
b. For a home with $3600 in annual taxes, what would you expect the selling price to be?
c. Calculate and interpret the coefficient of determination.
Predictor
Coefficient
SE of Coefficient
t
Intercept
326072.15
49.95
4.24
Tax
1.09107
0.05872
18.58
ANOVA
Source of Variation
SS
DF
MS
F
Regression
11984585
1
11984585
345.24
Error
3644994
105
34714
Total
15629579
106
Explanation / Answer
a) Regression equation:
Price = 326072.15 + 1.09107 (Tax)
b) For Tax = 3600,
Price = 326072.15 + 1.09107 (3600)
Price = $330000
c) Coefficient of determination = r2 = SSR/ SST = 11984585 / 15629579 = 0.7668
It indicates that 76.68% of variation in prices can be explained by tax charged.
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