For the following scores,
X  Y 
3  6 
6  1 
3  4 
3  3 
5  1 
a.
To Find: The regression equation for predicting Y from the X values.
The regression equation for predicting Y from the X values is
Given info:
The data represents the scores of X and Y.
Calculation:
The general regression equation for predicting Y from the X values is,
Where, parameter b is calculated as
Regression equation:
Squared deviations
The below table showing the calculations required for calculating correlation:
S.no.  X  Y  Deviation  Deviation square  Product  






1  3  6  1  3  1  9  3 
2  6  1  2  2  4  4  4 
3  3  4  1  1  1  1  1 
4  3  3  1  0  1  0  0 
5  5  1  1  2  1  4  2 
Sum/ average 
4  3  8  18  10 
So, the sum of product of deviation (SP) is
The value of regression coefficient is,
The value of the intercept of the regression equation is,
The regression equation is,
Thus, the regression equation is
b.
To find: The predicted Y values from the given X values.
The predicted Y values for the given X scores are:
X  Y  Predicted Y value 
3  6  4.25 
6  1  0.50 
3  4  4.25 
3  3  4.25 
5  1  1.75 
Calculation:
The regression equation for predicting Y from the X values is
Substitute the given X scores in the above calculated regression equation for getting the predicted Y values. The predicted Y values are showing in the below table:
X  Y  Predicted Y value (

3  6  4.25 
6  1  0.50 
3  4  4.25 
3  3  4.25 
5  1  1.75 
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