The following data set shows the entrance exam score? (Verbal GMAT) for each of
ID: 3366290 • Letter: T
Question
The following data set shows the entrance exam score? (Verbal GMAT) for each of eight MBA students along with his or her grade point average? (GPA) upon graduation.
GMAT : 310 300 270 280 360 270 300 290
GPA: 3.7 3.1 3.1 3.2 3.8 2.9 3.6 3.1
A linear regression on the data gives the equation below. Complete parts a through d below. Predicted GPA equals 0.500000 + 0.009454 (GMAT)
A) SST
B) Partition the total sum of squares into the SSR and SSE.
c. Calculate the sample coefficient of determination
d. Test the significance of the population coefficient of determination using ?=0.05.
E) Use technology to determine the? p-value for the? test, rounding to three decimal places.
Explanation / Answer
Regression Analysis: GPA versus GMAT
Regression Equation
GPA = 0.500 + 0.00945 GMAT
A,B] Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
GMAT 1 0.5318 0.53178 12.42 0.012
Error 6 0.2570 0.04283
Total 7 0.7887
Model Summary
S R-sq R-sq(adj) R-sq(pred)
0.206952 67.42% 61.99% 28.35%
C] coefficient of determination
R^2 = 0.6742
d,e] alpha = 0.05
pvalue = 0.012 < alpha =0.05
Reject H0.
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