Question

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 5.2 220

2 5.5 229

3 5.9 256

4 . 5.9 209

5 5.9 223

6 6.1 217

7 5.9 230

8 5.6 270

9 5.7 238

10 5.9 214

11 5.4 408

12 . 5.6 259

13 5.8 304

14 5.5 258

15 5.3 282

16 5.4 383

17 5.7 269

18 5.4 267

19 5.6 225

20 5.4 260

21 5.9 231

22 5.8 218

23 5.8 248

24 5.9 241

a. Find the least squares line for the data.

ModifyingAbove y with caretyequals=6.25546.2554plus+left parenthesis nothing right parenthesis−0.0023negative 0.0023x (Round to four decimal places as​ needed.) CORRECT ANSWER

b. Interpret β0 and β1 in the words of the problem. Interpret β0 in the words of the problem.

A.The regression coefficient β0 is the estimated sweetness index for orange juice that contains 0 ppm of pectin.

B.The regression coefficient β0 is the estimated increase​ (or decrease) in amount of pectin​ (in ppm) for each​ 1-unit increase in sweetness index.

C.The regression coefficient β0 is the estimated amount of pectin​ (in ppm) for orange juice with a sweetness index of 0.

D.The regression coefficient β0 does not have a practical interpretation.

Answer 1

Interpret β0 in the words of the problem.

A.The regression coefficient β0 is the estimated sweetness index for orange juice that contains 0 ppm of pectin