Question

6. Consider the following sample regression results:

Y hat = 15.4 + 2.20 X_{1} +
48.14
X_{2}
R^{2} = .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
b_{1}.

b. Is there evidence of a linear relationship
between X_{2} 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

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