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One manufacturer has developed a quantitative index of the "sweetness" of orange juice. (The higher the index, the sweeter the juice). Is there a relationship between the sweetness index and a chemical measure such as the amount of water-soluble pectin (parts per million) in the orange juice? Data collected on these two variables for 24 production runs at a juice manufacturing plant are shown in the accompanying table. Suppose a manufacturer wants to use simple linear regression to predict the sweetness (y) from the amount of pectin (x).
| Run | Sweetness_Index | Pectin_(ppm) |
| 1 | 5.1 | 220 |
| 2 | 5.4 | 229 |
| 3 | 6.1 | 259 |
| 4 | 5.9 | 210 |
| 5 | 5.7 | 226 |
| 6 | 5.9 | 214 |
| 7 | 5.9 | 232 |
| 8 | 5.5 | 267 |
| 9 | 5.5 | 240 |
| 10 | 5.9 | 211 |
| 11 | 5.5 | 411 |
| 12 | 5.6 | 257 |
| 13 | 5.8 | 307 |
| 14 | 5.5 | 260 |
| 15 | 5.3 | 286 |
| 16 | 5.4 | 385 |
| 17 | 5.7 | 271 |
| 18 | 5.4 | 261 |
| 19 | 5.6 | 229 |
| 20 | 5.3 | 262 |
| 21 | 5.9 | 234 |
| 22 | 5.8 | 219 |
| 23 | 5.8 | 244 |
| 24 | 5.9 | 239 |
a) Find the least squares line for the data.
b) Interpret B0 and B1 in the words of the problem.
c) Predict the sweetness index if the amount of pectin in the orange juice is 400 ppm.