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In a multiple linear regression how do we calculate the standard error of B2 ( we...

In a multiple linear regression how do we calculate the standard error of B2 ( we have two independent variables and a constant so we have B0 B1 and B2) how do we calculate the standard error of the three.

Expert Solution

Let the regression model be,

y_i = B0 + B1 x_1i + B2 x_2i , for i = 1,2,....n

Let the data be represented in matrix form as,

The residuals e is given as,

where I is the unit matrix.

The error standard deviation is estimated as,

where p is the number of coefficients. Here p = 2.

Let be the diagonal elements of the standard error matrix

The standard errors of B0 B1 and B2 are estimated as

orchestra answered 3 years ago

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