Question

A regression model relating units sold (Y), price (X1), and whether or not promotion was used (X2=1 if promotion was used and 0 if it was not ) resulted in the following model. Yhat=120-0.03X1+0.7X2 and the following information is provided. n=15 Sb1=.01 Sb2=0.1

a) Is a price significant variable?

b) Is promotion significant?

Answer 1

(A) test statistic for price = b1/Sb1

setting b1= -0.03 and Sb1 = 0.01

we get

test statistic t = -0.03/0.01 = -3

degree of freedom = n-2

= 15-2

= 13

Using t distribution table with test statistic (-3) and df(13) w

we get

p value = 0.0102

So, at 0.05 significance level, p value is significant because it is less than significance level of 0.05

Therefore, price is a significant variable at 0.05 significance level

(B)

test statistic for promotion = b2/Sb2

setting b2= 0.7 and Sb2 = 0.1

we get

test statistic t = 0.7/0.1 = 7

degree of freedom = n-2

= 15-2

= 13

Using t distribution table with test statistic (7) and df(13) w

we get

p value = 0.0000

So, at 0.05 significance level, p value is significant because it is less than significance level of 0.05

Therefore, promotion is a significant variable at 0.05 significance level