a. Correlation, Slope, and Y-intercept
r = .535, b = 2.0, a = 2.0
b. The regression equation is y´ = a +bx . a =
y-intercept, b = Slope, y´ =
predicted score for x.
Case |
X |
Y |
Y´ |
1 |
1 |
2 |
2.0+2.0(1) = 4 |
2 |
1 |
6 |
2.0+2.0(1) = 4 |
3 |
2 |
5 |
2.0+2.0(2) = 6 |
4 |
2 |
7 |
2.0+2.0(2) = 6 |
Sum |
|
|
|
Case |
X |
Y |
Y´ |
|
|
1 |
1 |
2 |
4 |
2-5 = -3 |
(-3)2 = 9 |
2 |
1 |
6 |
4 |
6-5 = 1 |
(1)2 = 1 |
3 |
2 |
5 |
6 |
5-5 = 0 |
(0)2 = 0 |
4 |
2 |
7 |
6 |
7-5 = 2 |
(2)2 = 4 |
Sum |
|
|
|
|
Σ = 14 |
Case |
X |
Y |
Y´ |
(Y - Y´) |
(Y
- Y´)2 |
1 |
1 |
2 |
4 |
2-4 = -2 |
(-2)2 = 4 |
2 |
1 |
6 |
4 |
6-4 = 2 |
(2)2 = 4 |
3 |
2 |
5 |
6 |
5-6 = -1 |
(-1)2 = 1 |
4 |
2 |
7 |
6 |
7-6 = 1 |
(1)2 = 1 |
Sum |
|
|
|
|
Σ = 10 |
h. The largest deviations are for Cases 1 and 2, and the size of the deviation is 2.The smallest deviations are for Cases 3 and 4, and the size of the deviation is 1.
i. See g above. Both values should be 10
j. SS Predicted Calculations
Case |
X |
Y |
Y´ |
|
|
1 |
1 |
2 |
4 |
4-5 = -1 |
(-1)2 = 1 |
2 |
1 |
6 |
4 |
4-5 = -1 |
(-1)2 = 1 |
3 |
2 |
5 |
6 |
6-5 = 1 |
(1)2 = 1 |
4 |
2 |
7 |
6 |
6-5 = 1 |
(1)2 = 1 |
Sum |
|
|
|
|
Σ = 4 |
l. See j above