For the following set of data,
X  Y 
7  6 
9  6 
6  3 
12  5 
9  6 
5  4 
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 values of X and Y.
Calculation:
The general regression equation for predicting Y from the X values is,
Where, parameter b is calculated as
The formula for SP is as follows:
The formulae for squared deviations
The below table showing the calculations required for calculating correlation:
S.no.  X  Y  Deviation  Deviation square  Product  






1  7  6  1  1  1  1  1 
2  9  6  1  1  1  1  1 
3  6  3  2  2  4  4  4 
4  12  5  4  0  16  0  0 
5  9  6  1  1  1  1  1 
6  5  4  3  1  9  1  3 
Sum/ average 
8  5  32  8  8 
So, the sum of product of deviation (SP) is 8,
Now substitute the above calculated values in a value then:
So, a value is calculated as 3 and b value is calculated as 2. Now substitute these values in the general regression equation then:
Thus, the regression equation is
b.
To calculate: The standard error of estimate for the equation.
The standard error of estimate for the equation is 1.22.
Calculation:
The Pearson correlation (r) is calculated as:
Substitute the above calculated values in the correlation formula then:
So, the Pearson correlation is 0.5.
The SS residual also known as unpredicted variability is calculated as:
Where r is calculated above as 0.5 as r^{2} is the squared correlation, so r^{2} is 0.25 and
So,
The standard error of estimate is calculated as:
Here SE is for standard error of estimate and
Now substitute the above calculated values in the standard error of estimate formula then:
Thus, the standard error of estimate is 1.22.
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