Question

The following equation is the sample regression line and numbers in the parentheses are the standard errors for coefficients.

?̂ = 5.40 + 3.74 ∗ X ,? 2 = 0.26, ??? = 6.2

(3.1) (2.0)

(a) Interpret the meaning of ?0 and ?1.

(b)Construct the Z statistics to calculate the P-value to test the ?0: ?1 = 1 vs. ?1 ≠ 1 at the 5% level? Can we reject the null hypothesis?

(c) Construct a 90% confidence interval for ?1.

Answer 1

a)

o tells us that for x=0 ; expected value of Y is 5.40

1 indicate that for 1 unit increase in value of x ; expected increase in value of Y is 3.74

b)

z statistic =(b1-1)/s_b1 =(3.74-1)/2 =1.37

for above test statistic ; p value =0.1706

as p value is greater than 0.05 level we can not reject the null hypothesis

c)

for 90% CI ; critical z =1.645

therefore 90% confidence interval =3.74 -/+1.645*2 = 0.45 to 7.03