Questions 1-17 are related to

Questions 1-17 are related to the following
Below are the values for two variablesx and y obtained from a sample of size 5.  We want tobuild 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 valueof 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 thepredicted y by,
a 6.017
b 5.785
c 5.563
d 5.349


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


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 (Definedas the average distance that the observed value falls from thepredicted line) = (28.61)1/2= 5.3488 ie 5.349

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