Regression Model in Deviated Form & Estimation of Parameters

 

Regression Model

in

Deviated Form

Manually computing multiple linear regression is time consuming and tedious. This can be improved by estimating the unknown parameters using a deviating equation rather than the original equation.

The deviated form is achieved by deviating the sample mean of response variable and predictors.

Consider the multiple linear regression Model with two regressors is given by:

The mean of the above regression model:

Estimation of Parameters

The OLS method is used to estimate the parameters of the deviated multiple linear regression model.

Consider the deviated regression model

Practice Question

given data

Y	X1	X2
30	4	10
20	3	8
36	6	11
24	4	9
40	8	12

Estimate the regression model  $Y = {\beta }_0 + {\beta }_1 X_1 + {\beta }_2 X_2 + \mathrm{u.\; Determine\; standard\; deviation\; and\; coefficient\; of\; determination.}$

Solution:

Y	X1	X2	X1 Y	X2 Y	X1 X2	Sqr X1	Sqr X2
30	4	10	120	300	40	16	100
20	3	8	60	160	24	9	64
36	6	11	216	396	66	36	121
24	4	9	96	216	36	16	81
40	8	12	320	480	96	64	144
150	25	50	812	1552	262	141	510

The Estimated Regression model in deviated form:

Standard deviation of regression model:

Coefficient of Determination: