1. A multiple regression model, Y = a + bX + cX 2 , is estimated by creating a n
ID: 3208502 • Letter: 1
Question
1. A multiple regression model, Y = a + bX + cX 2, is estimated by creating a new variable named “X2” that equals X 2 (X square). A computer package produces the following output:
a. Provide the estimated equation.
b. Test to see if the estimates of a, b, and c are statistically significant at the 5 percent significance level.
c. What is the exact level of significance for a, b, and c?
d. What is the fraction of total variation in Y that is explained by the regression equation?
e. Is the overall regression equation statistically significant at the 5 percent level? What is the exact level of significance of the equation as a whole?
f. If X is equal to 1,200, how much is Y?
DEPENDENT VARIABLE: Y R-SQUARE 0.8766 P-VALUE ON F 0.0001 F-RATIO OBSERVATIONS: 27 85.25 PARAMETER STANDARD ESTIMATE 8000.00 -12.00 0.005 VARIABLE ERROR T-RATIO P-VALUE 0.0325 0.0135 0.0197 INTERCEPT 3524.0 2.27 2.67 X2 0.002 2.50Explanation / Answer
a. Provide the estimated equation.
Y = 8000 - 12X + 0.005 X2
b. Test to see if the estimates of a, b, and c are statistically significant at the 5 percent significance level.
All three p-values are less than 0.05, we can conclude that the estimates of a, b, and c are statistically significant at the 5 percent significance level.
c. What is the exact level of significance for a, b, and c?
Level of significance for a is 0.0325, level of significance for b is 0.0135 and level of significance for c is 0.0197.
d. What is the fraction of total variation in Y that is explained by the regression equation?
R2 = 85.25%, this suggests 85.25% of total variation in Y that is explained by the regression equation.
e. Is the overall regression equation statistically significant at the 5 percent level? What is the exact level of significance of the equation as a whole?
P-value for F is smaller than 0.05, we can conclude that the overall regression equation is statistically significant at the 5 percent level. The exact level of significance of the equation as a whole is 0.0001.
f. If X is equal to 1,200, how much is Y?
Y = 8000 - 12X + 0.005 X2 = 8000 - 12(1200) + 0.005 (1200)2 = 800
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