Correlation and Regression Homework Solution
Correlation and Regression Homework Solution
1. Calculate the Pearson r for X and Y. Supply all values indicated. Use of Excel encouraged.
|X |Y |zx |zy |zx × zy |
|1 |5 |? |? |? |
|2 |2 |? |? |? |
|4 |4 |? |? |? |
|5 |1 |? |? |? |
[pic]= ?
[pic] = ?
sx = ?
sy = ?
n = ?
∑(zx zy) = ?
Pearson r = ?
|X |Y |X - Xbar |Y - Ybar |z_x |z_y |(z_x)(z_y) |
|2 |2 |-1 |-1 |-0.5477 |-0.5477 |0.3000 |
|4 |4 |1 |1 |0.5477 |0.5477 |0.3000 |
|5 |1 |2 |-2 |1.0954 |-1.0954 |-1.2000 |
|N |4 |
|N-1 |3 |
|Xbar |3 |
|Ybar |3 |
|stdev x |1.8257 |
|stdev y |1.8257 |
|Sum(zx zy) |-1.8 |
|Pearson r |-0.6 |
[pic]= (1/3) × (-1.20 + .30 + .30 + -1.20) = (1/3) × -1.80 = -0.60
2. What is the slope of the regression equation predicting Y from X?
Regression equation predicting Y from X is:
[pic]
Slope parameter (b) is equal to:
[pic]
To get intercept (a) parameter:
[pic]
[pic]
[pic]
Final regression equation:
[pic]
3. If X is 6, what is the predicted value of Y? (Show formula and answer.)
If x = 6:
[pic]
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