Question

Below is a partial computer output based on a sample of 40 observations.

	Coefficient	Standard Error
Constant	51.696	17.7
X1	-14.728	10.52
X2	180.864	50.24

Analysis of Variance
Source of Variation	Degrees of Freedom	Sum of Squares	Mean Square	F
Regression		19.412	9.706
Error			1,941.2

Required:

1. Use the output shown above and write the estimated regression equation.

2. Interpret the meaning of the coefficient of X₁ and X2.

3. Compute the test statistic required to know whether the parameter b₁ is significant.

Answer 1

A linear regression model that contains more than one predictor variable is called a multiple linear regression model. The following model is a multiple linear regression model with two predictor variables, and .

Given:
Constant coefficient is 51.696
Coefficient of x1   =-14.728
Coefficient of x2 = 108.864

1. Hence our regression line becomes:
  

2. Parameters and are referred to as partial regression coefficients. Parameter represents the change in the mean response corresponding to a unit change in when is held constant. Parameter represents the change in the mean response corresponding to a unit change in when is held constant.
That is here Y value will derease by 14.728 unit if x1 is increased one unit if coefficient of x2 stays constant
And Y value will inrease by 108.86 unit if x2 is increased one unit if coefficient of x1 stays constant.

The test is used to check the significance of individual regression coefficients in the multiple linear regression model.  The hypothesis statements to test the significance of a particular regression coefficient,

The test statistic for this test is based on the distribution (and is similar to the one used in the case of simple linear regression models in Simple Linear Regression Anaysis):

The analyst would fail to reject the null hypothesis if the test statistic lies in the acceptance region:

Fron the question we already know
  
Required test statistics to check the significance is