Question

onsider the following data:

UBI POH TLAM

120, 9, 21

60, 5, 16

18, 3, 12

21, 5, 12

85, 7, 17

60, 7, 16

(If you want to check data entry: sample covariance UBI, POH = 61.67; UBI, TLAM = 108.39)

a. What is the least squares linear regression equation when UBI is the dependent variable (Y) are X

variables two?

b. Which of the coefficients, if any, are significantly different from zero at the 90% level?

Answer 1

a.

The dependent and independent variables are as follows:

UBI (Y)	POH(x1)	TLAM(x2)
120	9	21
60	5	16
18	3	12
21	5	12
85	7	17
60	7	16

The following matrix and vector are defined in order to conduct the matrix calculation required to compute the estimated multiple regression coefficients:

Now, the vector with the estimated regression coefficients ​ is computed through the following matrix operation:

=

Now, for the values provided for and , we get that the vector with estimated regression coefficients is computed as follows:

=

Therefore, based on the data provided, the estimated multiple linear regression equation is:

b.

Here, we need to check which of the coefficients, if any, are significantly different from zero at the 90% level.

1 - = 0.90

= 0.90

And we know the p-value test.

p < . We reject the null hypothesis.

p > . We do not reject the null hypothesis.

Null Hypothesis :

Alternative Hypothesis :

The p-values corresponding to each coefficient are as follows:

Intercept 0.00566 < 0.01

POH 0.62132 > 0.01

TLAM 0.01226 > 0.01

Except intercept, all other coefficient are not significantly different from zero at the 90% level.