One manufacturer has developed a quantitative index of the​\"sweetness\" of orange juice.​ (The higher the​ index, the sweeterthe​ juice). Is there a relationship between the sweetness indexand a chemical measure such as the amount of​water-soluble pectin​(parts per​ million) in the orange​ juice? Data collected on thesetwo variables for 24 production runs at a juice manufacturing plantare shown in the accompanying table. Suppose a manufacturer wantsto use simple linear regression to predict the sweetness​ (y) fromthe 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+leftparenthesis nothing right parenthesis−0.0023negative 0.0023x (Roundto four decimal places as​ needed.) CORRECT ANSWER
b. Interpret β0 and β1 in the words of the problem. Interpret β0in the words of the problem.
A.The regression coefficient β0 is the estimated sweetness indexfor orange juice that contains 0 ppm of pectin.
B.The regression coefficient β0 is the estimated increase​ (ordecrease) in amount of pectin​ (in ppm) for each​ 1-unit increasein sweetness index.
C.The regression coefficient β0 is the estimated amount ofpectin​ (in ppm) for orange juice with a sweetness index of 0.
D.The regression coefficient β0 does not have a practicalinterpretation.
