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 | ||||
Answer:
| 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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