This is confusing me thank you for your help in advance Cons

This is confusing me, thank you for your help in advance!

Consider the EXPRESS data set (first 10 observations given). Use the complete data set in your analysis. Show the relevant output from Minitab in your answers. The first 10 observations are given for illustrative purposes.

a. Write out a complete general first-order model including an interaction term for Cost as the outcome.

b. Using Minitab, produce an output and write the least squares regression equation with the interaction term that was fit in Minitab.

c. State the null and alternative hypothesis to test if there is a significant interaction effect between weight and distance. Test the hypothesis at the ?= 0.01 level. Write your formal conclusion in terms of the variable names.

d. If there is a significant interaction effect, but the individual predictors (main effects) that make up that interaction are not significant in the model, would you suggest removing the main effects? Why or why not?

Weight Distance Cost 47 145 202 160 280 80 240 53 2.6 3.9 8 9.2 4.4 1.5 14.5 1.9 5.9 3.2 4.4 6.6 0.75 0.7 6.5 4.5 0.6 100 190 14 7.5

Solution

c)
Set Up Hypothesis
Null, No interaction effect between weight and distance,Ho: u1 = u2
Alternate, significant interaction effect between weight and distance - H1: u1 != u2
Test Statistic

Weight
X(Mean)=4.065
Standard Deviation(s.d1)=2.6434 ; Number(n1)=10

Disytance
Y(Mean)=149.7
Standard Deviation(s.d2)=79.494; Number(n2)=10
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =4.065-149.7/Sqrt((6.98756/10)+(6319.29604/10))
to =-5.79
| to | =5.79
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 9 d.f is 3.25
We got |to| = 5.79017 & | t | = 3.25
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -5.7902 ) = 0
Hence Value of P0.01 > 0,Here we Reject Ho

we colnclude that significant interaction effect between weight and distance