# 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

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 (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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