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). Click the icon to view the table. X Data regarding oranje juice sweetness a. Find the least squares line for the data. y= 6.2345+ (-0.0022)x (Round to four decimal places as needed.) b. Interpret, and, in the words of the problem. Interpret in the words of the problem. OA. The regression coefficient B is the estimated sweetness index for orange juice that contains 0 ppm of pectin. Run Sweetness Index Pectin (ppm) 1 5.1 222 2 5.5 225 3 5.9 258 4 5.9 212 5 5.8 222 6 6.1 214 7 5.9 233 OB. The regression coefficient B is the estimated increase (or decrease) in amount of pectin (in ppm) for each 1-unit increase in sweetness index. OC. The regression coefficient ẞo is the estimated amount of pectin (in ppm) for orange juice with a sweetness index of 0. 8 5.6 267 9 5.7 240 10 5.9 214 11 5.5 408 OD. The regression coefficient o does not have a practical interpretation. 12 5.6 258 13 5.9 308 14 5.6 256 15 5.4 287 16 5.2 380 17 5.7 274 18 5.5 261 19 5.8 229 20 5.2 261 21 5.8 231 22 5.7 222 23 5.9 246 24 5.9 241
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). Click the icon to view the table. X Data regarding oranje juice sweetness a. Find the least squares line for the data. y= 6.2345+ (-0.0022)x (Round to four decimal places as needed.) b. Interpret, and, in the words of the problem. Interpret in the words of the problem. OA. The regression coefficient B is the estimated sweetness index for orange juice that contains 0 ppm of pectin. Run Sweetness Index Pectin (ppm) 1 5.1 222 2 5.5 225 3 5.9 258 4 5.9 212 5 5.8 222 6 6.1 214 7 5.9 233 OB. The regression coefficient B is the estimated increase (or decrease) in amount of pectin (in ppm) for each 1-unit increase in sweetness index. OC. The regression coefficient ẞo is the estimated amount of pectin (in ppm) for orange juice with a sweetness index of 0. 8 5.6 267 9 5.7 240 10 5.9 214 11 5.5 408 OD. The regression coefficient o does not have a practical interpretation. 12 5.6 258 13 5.9 308 14 5.6 256 15 5.4 287 16 5.2 380 17 5.7 274 18 5.5 261 19 5.8 229 20 5.2 261 21 5.8 231 22 5.7 222 23 5.9 246 24 5.9 241
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter4A: Problems In Applying The Linear Regression Model
Section: Chapter Questions
Problem 2E
Related questions
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please answer in text form and in proper format answer with must explanation , calculation for each part and steps clearly
Transcribed Image Text: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).
Click the icon to view the table.
X
Data regarding oranje juice sweetness
a. Find the least squares line for the data.
y= 6.2345+ (-0.0022)x
(Round to four decimal places as needed.)
b. Interpret, and, in the words of the problem.
Interpret in the words of the problem.
OA. The regression coefficient B is the estimated sweetness index for orange juice that contains 0 ppm of pectin.
Run
Sweetness Index
Pectin (ppm)
1
5.1
222
2
5.5
225
3
5.9
258
4
5.9
212
5
5.8
222
6
6.1
214
7
5.9
233
OB. The regression coefficient B is the estimated increase (or decrease) in amount of pectin (in ppm) for each 1-unit increase in sweetness index.
OC. The regression coefficient ẞo is the estimated amount of pectin (in ppm) for orange juice with a sweetness index of 0.
8
5.6
267
9
5.7
240
10
5.9
214
11
5.5
408
OD. The regression coefficient o does not have a practical interpretation.
12
5.6
258
13
5.9
308
14
5.6
256
15
5.4
287
16
5.2
380
17
5.7
274
18
5.5
261
19
5.8
229
20
5.2
261
21
5.8
231
22
5.7
222
23
5.9
246
24
5.9
241
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