First, the reason for this question is that I believe that nutrition plays a part in a student's ability to focus and excel in school. If a student is eligible for subsidized lunch, likely they are not receiving healthy nutritious meals for breakfast and dinner. And a lower average family income is probably related to students' ability to receive subsidized lunches. However, other factors besides for average income contribute to eligibility; for that reason, test scores may be affected differently when compared to meal_pct and/or avginc.
The formula for this:
average test score = B0 + B1meal_pct + B2avginc + B3(meal_pct*avginc) + u
The formula for creating a variable representing the B3 component (interaction term):
gen stud_fin_state = meal_pct*avginc
A regression on JUST scores and meal_pct:
reg testscrmeal_pct, r
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Linear regression
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Number of
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obs =
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420
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F(1, 418)
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=
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1149.57
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Prob > F
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=
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0.0000
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R-squared
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=
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0.7548
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Root MSE
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=
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9.4467
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Robust
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testscr Coef.
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Std. Err.
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t
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P>t
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[95% Conf.
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Interval]
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meal_pct -.6102858
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.0179997
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-33.91
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0.000
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-.645667
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-.5749047
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_cons 681.4395
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.9853686
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691.56
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0.000
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679.5026
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683.3764
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Finally, the regression which will test for the interactive relationship:
reg testscrmeal_pctavgincstud_fin_state, r
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Linear regression
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Number of
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obs =
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420
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F(3, 416)
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=
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534.81
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Prob > F
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=
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0.0000
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R-squared
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=
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0.7820
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Root MSE
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=
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8.9279
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Robust
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testscr
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Coef.
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Std. Err.
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t
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P>t
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[95% Conf.
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Interval]
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meal_pct
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-.4607132
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.0341342
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-13.50
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0.000
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-.5278102
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-.3936162
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avginc
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.6188341
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.0753697
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8.21
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0.000
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.4706811
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.766987
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stud_fin_state
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-.0043107
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.0027813
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-1.55
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0.122
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-.0097779
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.0011564
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_cons
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667.6492
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2.030945
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328.74
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0.000
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663.657
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671.6414
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Based on what the two regressions show us, how can you interpret the coefficient on meal_pct? And the slight change between models one and two?
Is there a significant interactive relationship between the variables?
How could you visually (graphically) demonstrate?
Make sense out of that question and answer accordingly
Attachment:- Question.rar