A regression was performed on a sample of 20 observations. Two independent varia
ID: 3223363 • Letter: A
Question
A regression was performed on a sample of 20 observations. Two independent variables were included in the analysis, x and z. The relationship between x and z is z = x^2. The following estimated equation was obtained, y = 23.72 + 12.61x + 0.798z The standard errors for the coefficients are S_b1 = 4.85 and S_b2 = 0.21 For this model, SSR = 520.2 and SSE = 340.6 a. Estimate the value of y when x = 5. b. Compute the appropriate t ratios. c.Test for the significance of the coefficients at the 5% level. Which variable(s) is (are) significant? t_.025 = 2.11 d. Compute the coefficient of determination. Interpret the meaning of the coefficient of determination.Explanation / Answer
a. Value of y when x = 5
y^ = 23.72 + 12.61 x + 0.798 x
= 23.72 + 12.61 * 5 + 0.798 * 5 * 5 =
b. Sb1 = 4.85 and Sb2 = 0.21
SSR = 520.2 and SSE = 340.6
t - ratio for b1 = Coefficeint / Sb1 = 12.61/ 4.85 = 2.7
t - ratio for b2 = Coefficeint / Sb2 = 0.798/ 0.21 = 3.8
(c) t0.025 = 2.11 so we can say both t (b1) and t(b2) are significnat as their values are greater than t critical.
(d) Coefficient of determination = R2 = (520.2)/ ( 520.2 + 340.6) = 0.6043
The coefficient of determination telll that the proportion of the variance in the dependent variable that is predictable from the independent variables. So, in this case 60.44% is predicted by indepepndent variables .
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