Requirements
Write a program to calculate the linear regression size-estimating parameters for two arrays, each of n numbers. Enhance program 1 to work for the new calculations with minimal duplication.
Given a set of historical data for variables x and y, you want to determine if a likely value yk based on a known or estimated new value xk. An example would be the relationship between the estimated object LOC in a program and the actual new and changed program LOC.
Conditions
The historical x and y data must demonstrate a relationship.
There must be sufficient data produce a statistically significant result (at least three items and preferably five or more.)
Determine the beta0 and beta 1 parameters that best represent the relationship between these x and y data, and then calculate yk using the following formula and the available data.
Testing
Thoroughly test the program. At a minimum, use this program to calculate the beta parameters for the three provide data sets.
TEST DATA
| Program Number | Estimated Object LOC | Estimated New and Changed LOC | Actual New and Changed LOC |
|---|---|---|---|
| 1 | 130 | 163 | 186 |
| 2 | 650 | 765 | 699 |
| 3 | 99 | 141 | 132 |
| 4 | 150 | 166 | 272 |
| 5 | 128 | 137 | 291 |
| 6 | 302 | 355 | 331 |
| 7 | 95 | 136 | 199 |
| 8 | 945 | 1206 | 1890 |
| 9 | 368 | 433 | 788 |
| 10 | 961 | 1130 | 1601 |
| Sum | 3828 | 4632 | 6389 |
| Average | 382.8 | 463.2 | 638.9 |
- Use the data in above for estimated object LOC and actual new and changed LOC. The resulting values should be beta_0 = -22.55 and beta_1 = 1.7279.
- Calculate the beta_0 and beta_1 parameters for the regression fit of estimated new and changed LOC to actual new and changed LOC columns in Table D8. The answer in this case should be beta_0 = -23.92 and beta_1 = 1.4310.
- Calculate the beta_0 and beta_1 parameters for the estimated new and changed LOC and the actual new and changed LOC for the programs 2A, 3A and 4A that you have developed.
WORKED EXAMPLE
| Program Number | Estimated Object LOC | Estimated New and Changed LOC | XiYi | Xi2 |
|---|---|---|---|---|
| 1 | 1 | 130 | 186 | 24180 |
| 2 | 2 | 650 | 699 | 454350 |
| 3 | 3 | 99 | 132 | 13068 |
| 4 | 4 | 150 | 272 | 40800 |
| 5 | 5 | 128 | 291 | 37248 |
| 6 | 6 | 302 | 331 | 99962 |
| 7 | 7 | 95 | 199 | 18905 |
| 8 | 8 | 945 | 1890 | 1786050 |
| 9 | 9 | 368 | 788 | 289984 |
| 10 | 10 | 961 | 1601 | 1538561 |
| Sum | 3828 | 6389 | 4303108 | 2540284 |
| Average | 382.8 | 638.9 |