How well do exams given during the semester predict perfomance on the final? One class had 3 tests during the semester. Computer output of the regression gives:
Dependent varible is final
s = 13.46, R-square = 77.7%, R-sq(adj) = 74.1%
| Predictor |
Coeff |
SE(Coeff) |
t |
p-value |
| intercept |
-6.72 |
14.00 |
-0.48 |
0.636 |
| test 1 |
0.2560 |
0.2274 |
1.13 |
0.274 |
| test 2 |
0.3912 |
0.2198 |
1.78 |
0.091 |
| test 3 |
0.9015 |
0.2086 |
4.32 |
< 0.0001 |
Analysis of variance
| Source |
DF |
SS |
MS |
F |
P-value |
| Regression |
3 |
11961.8 |
3987.3 |
22.02 |
< 0.0001 |
| Error |
19 |
3440.8 |
181.1 |
|
|
| Total |
22 |
15402.6 |
|
|
|
a) write the equation of the regression model
b) how much of the variation in the final exam scores is acounted for by the regression model?
c) explain in context what the coefficient of test 3 scores means
d) a student argues that clearly the first exam doesn't help to predit final performance. She suggests that this exam not be given at all. Does Test 1 have no effect on the final exam score?