Question

In a multiple regression analysis, two independent variables are considered, and the sample size is 27. The regression coefficients and the standard errors are as follows.

b1 = 1.670	Sb1 = 0.52
b2 = ?2.018	Sb2 = 0.65

Conduct a test of hypothesis to determine whether either independent variable has a coefficient equal to zero. Would you consider deleting either variable from the regression equation? Use the 0.05 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

H0: ?1 = 0	H0: ?2 = 0
H1: ?1 ? 0	H1: ?2 ? 0
H0 is rejected if t < ?2.064 or t > 2.064

Answer 1

Let two independent variabl are x1 and X2 . And Y= dependent variable .

Regression line :

Here first testcoefficient of :

Hypothesis:      vs   

Test statistice formula:

So here t =3.212   >2.064   ; Reject H0 .

We conclude that ( variable X1) is significant .

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Test coefficient of :

Hypothesis:      vs   

Test statistics :

So here t =3.105   > 2.064   ; Reject H0 .

We conclude that ( variable X2) is significant .

None of the variable is delected .