Question

You are given the following data, where X1 (GRE total score) and X2 (undergraduate GPA) are used to predict Y (graduate GPA):

Y          X1       X2

3.6	135	2.6
4	130	2.6
3	105	2.4
3.3	115	2.7
3.2	105	3.1
3	100	3.2
2.7	110	3.8
3.8	125	3.6
4	145	3.2

Determine the following multiple regression values.

Report intercept and slopes for regression equation accurate to 3 decimal places:
    Intercept: a=
    Partial slope X1: b1=
    Partial slope X2: b2=


Report sum of squares accurate to 3 decimal places:
    SSreg=
    SSTotal=

Test the significance of the overall regression model (report F-ratio accurate to 3 decimal places and P-value accurate to 4 decimal places):
    F-ratio =
    P-value =

Report the variance of the residuals accurate to 3 decimal places:
    s2res=

Report the standard error of the partial slope estimate for GRE total along with the test statistic (report answers accurate to 3 decimal places):
    s(b1)=
    t1=

Answer 1

R Code

> y<-c(3.6,4,3,3.3,3.2,3,2.7,3.8,4)
> x1<-c(135,130,105,115,105,100,110,125,145)
> x2<-c(2.6,2.6,2.4,2.7,3.1,3.2,3.8,3.6,3.2)
> reg<-lm(y~x1+x2)
> summary(reg)

Call:
lm(formula = y ~ x1 + x2)

Residuals:
Min 1Q Median 3Q Max
-0.3760 -0.1186 -0.0393 0.1671 0.3134

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 0.709001 0.986610 0.719 0.49939   
x1 0.025744 0.006149 4.187 0.00577 **
x2 -0.122335 0.198772 -0.615 0.56086   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2699 on 6 degrees of freedom
Multiple R-squared: 0.7544,   Adjusted R-squared: 0.6726
F-statistic: 9.217 on 2 and 6 DF, p-value: 0.01481

Answers

Intercept: a= 0.709001
    Partial slope X1: b1=0.025744
    Partial slope X2: b2= -0.122335

F-statistic: 9.217 on 2 and 6 DF, p-value: 0.01481 =0.0418

SSE = 0.2699 =0.270

s(b1) =0.006149 =0.006 t1= 4.187