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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
Linear regression
Number of
obs =
420
F(1, 418)
=
1149.57
Prob > F
0.0000
R-squared
0.7548
Root MSE
9.4467
Robust
testscr Coef.
Std. Err.
t
P>t
[95% Conf.
Interval]
meal_pct -.6102858
.0179997
-33.91
0.000
-.645667
-.5749047
_cons 681.4395
.9853686
691.56
679.5026
683.3764
Finally, the regression which will test for the interactive relationship:reg testscrmeal_pctavgincstud_fin_state, r
F(3, 416)
534.81
0.7820
8.9279
testscr
Coef.
meal_pct
-.4607132
.0341342
-13.50
-.5278102
-.3936162
avginc
.6188341
.0753697
8.21
.4706811
.766987
stud_fin_state
-.0043107
.0027813
-1.55
0.122
-.0097779
.0011564
_cons
667.6492
2.030945
328.74
663.657
671.6414
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
Verified Expert
Multiple regression analysis is almost the same as simple linear regression. The only difference between simple linear regression and multiple regression is in the number of predictors (“x” variables) used in the regression. Simple regression analysis uses a single x variable for each dependent “y” variable.
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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.
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LINEAR PROGRAMMING MODELS
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