Question

The admissions officer for Clearwater College developed the following estimated regression equation relating the final college GPA to the student's SAT mathematics score and high-school GPA. y = -1.4053 +.023501 +.004932 where 21 = high-school grade point average 22 = SAT mathematics score y = final college grade point average Round your answers to 4 decimal places. a. Complete the missing entries in this Excel Regression tool output. Enter negative values as negative numbers. ANOVA of SS M S F Significance F 1.7621 Regression Residual Total 1.88 Stat P-value Intercept Coefficients -1.4053 0.0235 0.0049 Standard Error 0.4848 0.0087 0.0011 X1 X2

Answer 1

a)

df(regression)=2

df(residual)=10-2-1=7

SS(residual)=1.7621-0.1.88=0.1179

MS=SS/df

F=0.8811/0.0168=52.3100

t statistic=b₁/s_b1

p-value=tdist(t,7,2)

	df	SS	MS	F	significance F
Regression	2	1.7621	0.8811	52.3100	0.0000
residual	7	0.1179	0.0168
Total	9	1.88
	Coefficients	standard error	t stat	p-value
Intercept	-1.4053	0.4848	-2.8987	0.0230
X1	0.0235	0.0087	2.7011	0.0306
X2	0.0049	0.0011	4.4545	0.0030

b)

p-value is less than 0.05,so regression model is significant.

c)

R^2=1.7621/1.88=0.9373

As,93.73% of the variation is explained by the model,so,yes,it provides good fit.

d)

As,p-value for both slope coefficients is less than 0.05,so both coefficients are significant.