The numbers at below represent a sample of 50 data pairs in protein residue analysis. In this case a presence of an antibody residue (the X-variable) was paired with antigen residue (the Y-variable) in an attempt to find a good predictor of the antigen.
Instructions: Use regression analysis to compare the antibody residue to the antigen residue, and answer the following questions:
A) What is the p-value of the regression?
B) Can you reject the null hypothesis that there is no relationship between the variables at the 99% confidence level?
C) What is the regression line?
D) What percentage of the response variable is explained by the predictor variable?
E) If 10 antibodies were found, what would be the predicted number of antigens?
| Y |
|
X |
| 6.232219 |
|
4.968847 |
| 6.61337 |
|
4.387175 |
| 6.181807 |
|
4.313497 |
| 9.665825 |
|
4.532325 |
| 10.12078 |
|
4.857142 |
| 6.709896 |
|
5.738545 |
| 5.955607 |
|
1.372892 |
| 5.804289 |
|
4.851473 |
| 5.825796 |
|
5.109552 |
| 7.583615 |
|
6.137843 |
| 6.418141 |
|
1.653975 |
| 6.565613 |
|
3.718583 |
| 8.095048 |
|
7.565812 |
| 6.266192 |
|
5.410496 |
| 7.449414 |
|
3.990631 |
| 5.884781 |
|
5.817375 |
| 5.848578 |
|
5.38294 |
| 7.322495 |
|
1.959916 |
| 4.979823 |
|
4.798227 |
| 6.995607 |
|
3.684112 |
| 9.309947 |
|
6.198947 |
| 6.256845 |
|
5.288981 |
| 8.221402 |
|
2.185233 |
| 6.636983 |
|
4.717766 |
| 6.13748 |
|
3.737241 |
| 9.219266 |
|
4.385324 |
| 7.549079 |
|
5.585259 |
| 7.559128 |
|
5.746056 |
| 6.505517 |
|
2.87724 |
| 4.711737 |
|
2.117368 |
| 7.631921 |
|
6.91073 |
| 8.079841 |
|
7.307294 |
| 9.335665 |
|
6.713304 |
| 8.594437 |
|
8.899871 |
| 4.064386 |
|
3.715086 |
| 6.940746 |
|
2.861196 |
| 9.378046 |
|
7.560924 |
| 6.792001 |
|
6.888018 |
| 7.847573 |
|
3.358733 |
| 7.063549 |
|
4.703238 |
| 6.892548 |
|
2.138218 |
| 7.249766 |
|
7.496487 |
| 6.67047 |
|
5.186585 |
| 6.406282 |
|
1.487942 |
| 6.180074 |
|
4.290956 |
| 4.190021 |
|
1.260188 |
| 5.991209 |
|
1.835718 |
| 10.31955 |
|
9.230183 |
| 4.713792 |
|
2.137921 |
| 6.41826 |
|
1.655635 |