Question

The quality of the orange juice produced by a manufacturer 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 30 production runs at a juice manufacturing plant are shown in the table. Suppose a manufacturer wants to use simple linear regression to predict the sweetness from the amount of pectin. Perform the linear regression analysis and answer the following questions.

Run	Sweetness Index	Pectin (PPM)
1	5.2	225
2	5.6	230
3	6	262
4	6	215
5	5.8	227
6	6.1	220
7	5.8	234
8	5.7	273
9	5.6	243
10	6	211
11	5.4	414
12	5.7	259
13	5.8	309
14	5.6	262
15	5.3	279
16	5.4	386
17	5.7	274
18	5.6	261
19	5.7	224
20	5.4	266
21	5.9	235
22	5.9	220
23	5.8	249
24	6	241
25	6.1	209
26	6.3	214
27	6.9	223
28	7	212
29	7.5	235
30	8	199

1. Is the whole regression model significant in predicting the sweetness of orange juice? Make sure to show which values you use to make the decision.

2. Write down the regression model using the actual values from regression analysis and actual names of the variables.

3. What is the value of the estimated slope? Interpret the value of the estimated slope in terms of orange juice sweetness and amounts of pectin.

4. What is the value of the estimated intercept? Interpret the value in terms of orange juice sweetness and amounts of pectin.

5. If the amount of pectin is decreased by 5 units, how will the sweetness of the orange juice change?.

Answer 1