Regression Analysis: Avg. Tot. Score versus %Takers, T/S Ratio Model Summary S R
ID: 3155738 • Letter: R
Question
Regression Analysis: Avg. Tot. Score versus %Takers, T/S Ratio
Model Summary
S R-sq R-sq(adj) R-sq(pred)
34.2385 79.91% 79.06% 76.83%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 1118.5 39.5 28.34 0.000
%Takers -2.547 0.187 -13.62 0.000 1.05
T/S Ratio -3.73 2.21 -1.69 0.098 1.05
1. What are the degrees of freedom associated with the t tests of the slopes?
A) 46
B) 47
C) 48
D) 49
E) 50
2.Under what conditions are the computed p-values for these tests valid?
Explanation / Answer
1. Under the null hypothesis, H0 that the population regression coefficient is , Prof. R.A. Fisher proved that the statistic
t = (b-) [ (n-2) ( xi - X)2 / (yi - Y)2] 1/2 follows Student's t distribution with n-2 degrees of freedom. Here the vaule of n is not given. If n=50, then, df = 50-2 = 48.
2. The value of p is calculated based on the percentage of permissible error, whether it is 5% or 1%.