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.)

b. Interpret

ModifyingAbove beta with caret 0β0

and

ModifyingAbove beta with caret 1β1

in the words of the problem.Interpret

ModifyingAbove beta with caret 0β0

in the words of the problem.

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

B.The regression coefficient ModifyingAbove beta with caret 0β0is the estimated increase​ (or decrease) in amount of pectin​ (in ppm) for each​1-unit increase in sweetness index.Your answer is not correct.

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

D.The regression coefficient ModifyingAbove beta with caret 0β0 does not have a practical interpretation.This is the correct answer.

Interpret β1in the words of the problem.

A.The regression coefficient β1 is the estimated increase​ (or decrease) in amount of pectin​ (in ppm) for each​1-unit increase in sweetness index.

B.The regression coefficient ModifyingAbove beta with caret 1β1 is the estimated sweetness index for orange juice that contains 0 ppm of pectin.

C.The regression coefficient ModifyingAbove beta with caret 1β1 is the estimated increase​ (or decrease) in sweetness index for each​ 1-unit increase in pectin.This answer is correct.

D.The regression coefficientModifyingAbove beta with caret 1β1does not have a practical interpretation.c. Predict the sweetness index if the amount of pectin in the orange juice is 350 ppm.The predicted sweetness index is

________.​(Round to four decimal places as​ needed.)

Answer 1