For the following set of data,
To Find: The regression equation for predicting Y from the X values.
The regression equation for predicting Y from the X values is .
The data represents the values of X and Y.
The general regression equation for predicting Y from the X values is,
Where, parameter b is calculated as and parameter a calculated as
The formula for SP is as follows:
The formulae for squared deviations and are as follows:
The below table showing the calculations required for calculating correlation:
So, the sum of product of deviation (SP) is 8, is 32 and is 8. Now substitute the above calculated values in the b value then:
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 .
To calculate: The standard error of estimate for the equation.
The standard error of estimate for the equation is 1.22.
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 r2 is the squared correlation, so r2 is 0.25 and is calculated above as 8. Substitute these values in the formula then:
So, is computed as 6.
The standard error of estimate is calculated as:
Here SE is for standard error of estimate and is degree of freedom calculated as:
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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