Homework SourseThe following data show the number of hours studied for an e
The following data show the number of hours studied for an exam, x, and the grade received on the exam, y (y is measured in 10\'s; that is, y = 8 means that the grade, rounded to the nearest 10 points, is 80).
Calculate the estimated standard error of regression, sb1, for the number of hours studied–exam grade relationship explained above. (Give your answer correct to four decimal places.)
| x | 2 | 2 | 3 | 3 | 3 | 4 | 5 | 5 | 5 | 6 | 7 | 7 | 8 | 8 | 8 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| y | 5 | 6 | 5 | 7 | 8 | 5 | 6 | 9 | 10 | 8 | 9 | 10 | 8 | 9 | 10 |
Solution
First let us find the regression line equation
y = 4.538+0.618x
SE = sb1 = sqrt [ (yi - i)2 / (n - 2) ] / sqrt [ (xi - x)2 ]
= sq rt [var(y)n/(n-2) ]/sq rtnvar(x)
= sq rt[3.524/13]/sq rt 4.781
= 0.23811
| X | Y | XY | XX |
| 2 | 5 | 10 | 4 |
| 2 | 6 | 12 | 4 |
| 3 | 5 | 15 | 9 |
| 3 | 7 | 21 | 9 |
| 3 | 8 | 24 | 9 |
| 4 | 5 | 20 | 16 |
| 5 | 6 | 30 | 25 |
| 5 | 9 | 45 | 25 |
| 5 | 10 | 50 | 25 |
| 6 | 8 | 48 | 36 |
| 7 | 9 | 63 | 49 |
| 7 | 10 | 70 | 49 |
| 8 | 8 | 64 | 64 |
| 8 | 9 | 72 | 64 |
| 8 | 10 | 80 | 64 |
| 76 | 115 | 624 | 452 |
