The SAT has gone through many revisions over the years. People argue that female students generally...

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The SAT has gone through many revisions over the years. Peopleargue that female students generally do worse on math tests butbetter on writing tests. Consider the following portion of data on20 students who took the SAT test last year. Information includeseach studentâ€™s score on the writing and math sections of the exam,the studentâ€™s GPA, and a Female dummy variable that equals 1 if thestudent is female, 0 otherwise.
Writing Math GPA Gender
620 600 3.44 0
570 550 3.04 0
540 540 2.67 0
580 610 3.29 0
590 590 3.36 0
550 520 2.88 1
580 610 3.20 0
480 510 2.30 0
590 570 3.17 1
620 660 3.71 0
530 520 2.38 0
610 600 3.25 1
600 530 3.13 1
640 580 3.51 1
540 570 2.82 1
540 500 2.38 0
560 620 3.39 0
550 540 2.73 0
540 590 3.03 0
540 520 2.84 0
a-1. Estimate a linear regression model withmath score as the response variable and GPA and the female dummyvariable as the explanatory variables. (Negative valuesshould be indicated by a minus sign. Round your answers to 2decimal places.)
MathË†Math^ = ___ + _ GPA + ___Female.
a-2. Compute the predicted math score for amale and female student with a GPA of 3.5. (Roundcoefficient estimates to at least 4 decimal places and final answerto 2 decimal places.)
MathË†Math^
Male student
Female student

Answer & Explanation Solved by verified expert

3.9 Ratings (569 Votes)

using excel data analysis tool for regression,steps are: write data>menu>data>data analysis>regression>enter required labels>ok> and following o/p is obtained

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.886468
R Square	0.785825
Adjusted R Square	0.760628
Standard Error	21.31292
Observations	20

ANOVA
	df	SS	MS	F	Significance F
Regression	2	28332.91	14166.46	31.18714	2.05E-06
Residual	17	7722.086	454.2403
Total	19	36055

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	274.1203	37.84651	7.242949	1.37E-06	194.2712	353.9695	194.2712	353.9695
GPA	98.71444	12.54348	7.869781	4.56E-07	72.25001	125.1789	72.25001	125.1789
Gender	-21.1008	10.55492	-1.99915	0.061839	-43.3698	1.168104	-43.3698	1.168104

a-1)

MathË†Math^ = 274.12 + 98.71 GPA - 21.10 Female.

a-2)

for female,

MathË†Math^ = 274.12 + 98.71 *3.5 - 21.10 *1 = 598.52

-----

for male

.MathË†Math^ = 274.12 + 98.71 *3.5 - 21.10 *0 = 619.62

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Writing	Math	GPA	Gender
620	600	3.44	0
570	550	3.04	0
540	540	2.67	0
580	610	3.29	0
590	590	3.36	0
550	520	2.88	1
580	610	3.20	0
480	510	2.30	0
590	570	3.17	1
620	660	3.71	0
530	520	2.38	0
610	600	3.25	1
600	530	3.13	1
640	580	3.51	1
540	570	2.82	1
540	500	2.38	0
560	620	3.39	0
550	540	2.73	0
540	590	3.03	0
540	520	2.84	0