In: Statistics and Probability
The following sample observations were randomly selected:
1 | 2 | 3 | 4 | 5 | |
X: | 15 | 8 | 9 | 12 | 8 |
Y: | 25 | 22 | 16 | 16 | 14 |
a. Not available in Connect.
b. Determine the regression equation. (Negative answer should be indicated by a minus sign. Do not round intermediate calculations. Round the final answers to 4 decimal places.)
b =---- a =----
Y' = -----+----- X
c. Determine the value of Y' when
X is 26. (Do not round intermediate calculations.
Round the final answer to 4 decimal places.)
Solution =
X | Y | XY | X^2 | Y^2 |
15 | 25 | 375 | 225 | 625 |
8 | 22 | 176 | 64 | 484 |
9 | 16 | 144 | 81 | 256 |
12 | 16 | 192 | 144 | 256 |
8 | 14 | 112 | 64 | 196 |
n | 5 |
sum(XY) | 999.00 |
sum(X) | 52.00 |
sum(Y) | 93.00 |
sum(X^2) | 578.00 |
sum(Y^2) | 1817.00 |
Numerator | 159.00 |
Denominator | 284.77 |
r | 0.5583 |
r square | 0.3117 |
Xbar(mean) | 10.4000 |
Ybar(mean) | 18.6000 |
SD(X) | 2.7276 |
SD(Y) | 4.1761 |
b | 0.8548 |
a | 9.7097 |
The regression equation,
b = 0.8548 , a = 0.7097
= a + bx
= 0.7097 + (0.8548)x
Answer : = 0.7097 + (0.8548)x
Given,
The value of Y' when X is 26
= 0.7097 + (0.8548)x
= 0.7097 + (0.8548 * 26)
= 0.7097 + 22.2248
= 22.9345
Answer : = 22.9345