Question

The SAT has gone through many revisions over the years. People argue that female students generally do worse on math tests but better on writing tests. Consider the following portion of data on 20 students who took the SAT test last year. Information includes each student’s score on the writing and math sections of the exam, the student’s GPA, and a Female dummy variable that equals 1 if the student 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 with math score as the response variable and GPA and the female dummy variable as the explanatory variables. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

MathˆMath^ = _______ + _______ GPA + _____Female.

a-2. Compute the predicted math score for a male and female student with a GPA of 3.5. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

	MathˆMath^
Male student
Female student

Answer 1

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)

MathˆMath^ = 274.12 + 98.71 GPA - 21.10 Female.

a-2)

for female,

MathˆMath^ = 274.12 + 98.71 *3.5 - 21.10 *1 = 598.52

-----

for male

.MathˆMath^ = 274.12 + 98.71 *3.5 - 21.10 *0 = 619.62