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 +.0049.22 where x = high-school grade point average 19 = 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 55 MS Significance F Regression 1.7621 Residual Total 1.88 t Stat P-value Intercept Coefficients -1.4053 0.0235 0.0049 Standard Error 0.4848 0.0087 0.0011 X2 b. Using a = .05, test for overall significance. - Select your answer - c. Did the estimated regression equation provide a good fit to the data? Explain. - Select your answer - d. Use the t test and a = .05 to test Ho: B1 = 0 and Ho:B2 = 0. Use t table. The input in the box below will not be graded, but may be reviewed and considered by your instruction. blank

Answer 1

ANOVA F 52.3100 Significance F 0.0001 Regression Residual Total MS 0.8811 0.0168 2 7 1.7621 0.1179 .8800 9 1 t Intercept x1 x2 Coefficients Standard Error -1.4053 0.4848 0.0235 0.0087 0.0049 0.0011 Stat -2.8987 2.7011 4.4545 P-value 0.0230 0.0306 0.0030

MS = SS/df

df1 = k-1 , df2 = N-k

for regression df1 = k, df2 =N-k-1

t = coeff/standard error

for two-tailed

p-value = P(t > |TS|)

= t.inv.2t(abs(TS),df)

b) since p-value < alpha
the model is significant

c)
yes
d)
p-value for x1 = 0.0306 and for x2, it is 0.003
since p-value < alpha
both variables are significant