A men’s cologne company wants to investigate how its rating in a local magazine

Question

A men’s cologne company wants to investigate how its rating in a local magazine (X1), average monthly income in the area (in 100 dollars) (X2), and monthly advertising (in 100 dollars) (X3) is related to monthly sales (in 100 dollars). The dependent variable is monthly sales (in 100 dollars). Based on 350 observations, the following regression equation is estimated (=0.05):

Y= 34.56 + 12.36X1 + 6.54 X2 + 7059 X3

S(b0) = 3.58         s(b1)= 2.68         s(b2)= 3.06         s(b3)=723.54

SSR = 61.28       SSE= 12.36

Which of the regression coefficients are significant?

What is Fcalc for the given regression model?

What is the 95% confidence interval for b2?

Explanation / Answer

First we find the critical values. The degree of freedom is 348 and the level of significance is 5%. We use excel function and get the critical value as - 1.967 and + 1.967.

Degrees of freedom = n – 2 = 350 – 2 = 348

If the test statistics for the coefficient falls in between -1.967 and + 1.967 then we can say that the regression coefficient is insignificant and if it falls outside this interval then we conclude that the regression coefficient is significant.

First Part:

X1 = Average monthly income:

t = 12.36 / 2.68 = 4.612

Here the calculated t falls outside that above mentioned interval, so we conclude that the regression coefficient for the variable Average monthly income is significant here.

X2 = Monthly Advertising:

t = 6.54 / 3.06 =2.137

Here the calculated t falls outside that above mentioned interval, so we conclude that the regression coefficient for the variable Monthly Advertising s significant here.

X3 = Monthly Sale

t = 7059/ 723.54= 9.756

Here the calculated t falls outside that above mentioned interval, so we conclude that the regression coefficient for the variable Monthly Sale is significant here.

Second Part:

df for SSE = k = 3

df for SSE = n – k – 1 = 350 – 3 – 1 = 346

F = (SSR/df)/(SSE/df) = (61.28/3)/(12.36/346) = 571.814

F = 571.814

Third part:

Confidence interval:

b2 (-/+) E

E = tc *SE = 1.967 * 3.06

6.54 (-/+)6.0190

Þ (6.54 – 6.0190) and (6.54 + 6.0190)

Þ 0.521 and 12.559

The 95% confidence interval for b2 is (0.521 to 12.559)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.