Question

Questions 1-17 are related to the following
Below are the values for two variables x and y obtained from a sample of size 5.  We want to build a regression equation based the sample data.

	y	x
	18	5
	25	10
	9	5
	30	15
	46	18

7	The prediction error for the largest value of x is,
a	3.88
b	3.98
c	4.09
d	4.19
8	Sum of prediction errors is,
a	1.03
b	0.08
c	0.02
d	0
9	Sum of squared errors (SSE) is,
a	84.11
b	85.83
c	88.06
d	90.35
10	The variance of the prediction error is,
a	27.981
b	28.610
c	29.354
d	30.117
11	On average the observed y deviate from the predicted y by,
a	6.017
b	5.785
c	5.563
d	5.349

Answer 1

	x	y	xy	X sqr
	5	18	90	25
	10	25	250	100
	5	9	45	25
	15	30	450	225
	18	46	828	324
sum	53	128	1663	699

The normal equations are :

Sigma y = na + b Sigma x

Sigma XY = a Sigma X + B Sigma X square

n=5

Putting the values we get the two equations

128= 5a + 53b

1663 = 53a + 699 b

Solving as simultaneous equations we get a= 1.96 and b=2.23

The Regression line is therefore, y = 1.96 + 2.23X

We will use this line now.

1)The prediction for largest value of X is y predicted = 1.96 +2.23*18 = 42.1

The error= 46-42.1 = 3.9 The closest answer is 3.88

2) The sum of prediction errors is always zero

3) The sumof squared errors is 85.8299 ie 85.83

4) The variance of prediction errors = SSE /n-2 = 85.83 /3 = 28.61

5) This is given by the standard error of the estimate (Defined as the average distance that the observed value falls from the predicted line) = (28.61)^1/2= 5.3488 ie 5.349