Question

DATA 2

ID	X1	X2	X3	Y
A	0	2	4	9
B	1	0	8	10
C	0	1	0	5
D	1	1	0	1
E	0	0	8	10

CORRELATION MATRIX

	Y	X1	X2	X3
Y	1	?	-0.304	+0.889
X1	?	1	-0.327	0
X2	-0.304	-0.327	1	-0.598
X3	+0.889	0	-0.598	1

1. What is the mean squared error of the full model? (Correct answer is 4, please show me how to get there)

2.What is the typical deviation when you use the full model to predict scores on Y in the sample? (Correct answer is 0.89, please show me how to get there)

Answer 1

R code and output

y=c(9,10,5,1,10)
x1=c(0,1,0,1,0)
x2=c(2,0,1,1,0)
x3=c(4,8,0,0,8)
x=rbind(y,x1,x2,x3)
cor(t(x))
y x1 x2 x3
y 1.0000000 -0.3478042 -0.3035884 0.8890009
x1 -0.3478042 1.0000000 -0.3273268 0.0000000
x2 -0.3035884 -0.3273268 1.0000000 -0.5976143
x3 0.8890009 0.0000000 -0.5976143 1.0000000
fit=lm(y~x1+x2+x3)
summary(fit)

Call:
lm(formula = y ~ x1 + x2 + x3)

Residuals:
1 2 3 4 5
-1.49e-16 1.00e+00 1.00e+00 -1.00e+00 -1.00e+00

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.0000 2.8868 1.039 0.488
x1 -2.0000 2.0000 -1.000 0.500
x2 1.0000 1.6330 0.612 0.650
x3 1.0000 0.3227 3.098 0.199

Residual standard error: 2 on 1 degrees of freedom
Multiple R-squared: 0.9355, Adjusted R-squared: 0.7419
F-statistic: 4.833 on 3 and 1 DF, p-value: 0.3199

anova(fit)
Analysis of Variance Table

Response: y
Df Sum Sq Mean Sq F value Pr(>F)
x1 1 7.5 7.5 1.875 0.4016
x2 1 12.1 12.1 3.025 0.3322
x3 1 38.4 38.4 9.600 0.1987
Residuals 1 4.0 4.0   
y1=3-2*x1+x2+x3
y1
[1] 9 9 4 2 11