Question

6.    Consider the following sample regression results:

            Y hat = 15.4 +    2.20 X₁   + 48.14 X₂                 R² = .355

                     (6.14)     (.42)          (5.21)            n = 27

The numbers in the parentheses are the estimated standard errors of the sample regression coefficients.

6. (continued)

a.    Construct a 95% confidence interval for b₁.

b.    Is there evidence of a linear relationship between X₂   and Y at the 5% level of significance?

c.    If you were to use a global test to determine if this model had explanatory power, what would your CRITICAL value be if alpha = .01?

Answer 1

a)p=independent variables =2

here for (n-p-1=27-2-1=24) degree of freedom ; for 95% CI crtiical value of t=2.064

therefore 95% confidence interval for b1 =estimated mean -/+ t*std error=2.20-/+2.064*0.42

=1.333 ;3.067

b)

hee for significance test between X2 and Y:

Ho: 2=0

Ha:  20

for 0.05 level and (n-p-1=27-2-1=24) degree of freedom critical value t=2.064

Decision rule: reject Ho if test statistic |t| >2.064

here test statistic t=coefficient/standard error=48.14/5.21=9.24

as test statsitic falls in rejection region we reject null hypothesis

and conclude that there is evidence of a linear relationship between X2   and Y at the 5% level of significance.

c)

here for (p,n-p-1 =2,24) degree of freedom r CRITICAL value for global F test and 0.01 level of significance =5.614