The quality of the orange juice produced by a manufacturer (e.g., Minute Maid, Tropicana) is constantly monitored. There are numerous sensory and chemical components that combine to make the best tasting orange juice. For example, 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 table below. Suppose a manufacturer wants to use simple linear regression to predict sweetness (y) from the amount of pectin (x).

a.Find the least squares line for the data

b.Interpret and in the words of the problem

c.Predict the sweetness index if amount of pectin in the orange juice is 300ppm

Please refer below table:

RUN SWEETNESS INDEX PECTIN (ppm)

1 5.2 220

2 5.5 227

3 6 259

4 5.9 210

5 5.8 224

6 6 215

7 5.8 231

8 5.6 268

9 5.6 239

10 5.9 212

11 5.4 410

12 5.6 256

13 5.8 306

14 5.5 259

15 5.3 284

16 5.3 383

17 5.7 271

18 5.5 264

19 5.7 227

20 5.3 263

21 5.9 232

22 5.8 220

23 5.8 246

24 5.9 241