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I am learning multiple regression with categorical variables and in a book I came across this problem.

For yield of corn suppose there are two factors affecting, nitrogen level and depth of ploughing. Say there are three nitrogen categories(1,2,3) and two depth categories(1,2).

There's a interaction term of nitrogen*depth as well.

If the introduced dummy variables are as
$E_{i1}=1 $ if ith observation has nitrogen level 1 ,0 otherwise.
$E_{i2}=1 $ if ith observation has nitrogen level 2 ,0 otherwise.

And $D=1 $ if depth category is 1,0 otherwise .

Then the model would be
$Y=\beta_0+\beta_1E_1+\beta_2E_2+\beta_3D+\beta_4[E_1.D]+\beta_5[E_2.D]+\epsilon$.
Is this correct?

When the t-statistics are found for the category $[nitrogen=1*depth=1]$ significance value was 0.029 and for$ [nitrogen=2*depth=1]$ it was 0.290.
I was asked to interpret if the interaction term significantly affects the yield of corn.

Under 5% confidence level clearly the coefficient of the variable $[nitrogen=2*depth=1]$ is not significant. But since the coefficient of the variable $[nitrogen=1*depth=1]$ is significant can I say that, the interaction term significantly affects the yield of corn.
If both had insignificant coefficients then I could have said that there isn't a significant effect from the interaction term right?

Since the interaction term $[nitrogen=2*depth=1]$ had a insignificant coefficient then my fitted model would be $\hat Y=\hat\beta_0+\hat\beta_1E_1+\hat\beta_2E_2+\hat\beta_3D+\hat\beta_4[E_1.D]$

leaving out E2D.IS this correct?
Can someone please help me to figure this out.

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  • $\begingroup$ You could test the entire interaction with a single partial F test. $\endgroup$ – Glen_b Jul 2 '14 at 13:54
  • $\begingroup$ @Glen_b doesn't the F-test represent how the variables nitrogen,depth and nitrogen*depth all taken together describe the variation in Y?Not their individual influence right? $\endgroup$ – clarkson Jul 2 '14 at 15:42
  • $\begingroup$ Right - it directly answers this issue: "interpret if the interaction term significantly affects the yield of corn." $\endgroup$ – Glen_b Jul 2 '14 at 22:05

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