Question

1. 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.

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 points).

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

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 (2 points).

4. What is the value of the estimated intercept? Interpret the value in terms of orange juice sweetness and amounts of pectin (2 points).

5. If the amount of pectin is decreased by 5 units, how will the sweetness of the orange juice change? (2 points).

6. Write down the null and alternative hypotheses for the influence of individual variable “Pectin (PPM)” on the sweetness of the orange juice (2 points).

7. What are the statistical values that should be used to make a decision about the rejection of H₀ from a previous question? Use alpha of 0.05. Show an actual value from the regression analysis output (2 points).

8. Find a t-critical for the influence of Pectin (PPM) on the sweetness. Use the alpha of 0.1 (2 points).

9. Does the amount of pectin significantly predict the sweetness of the orange juice? Explain why you have made this conclusion and which numbers you have used to do so. Use the alpha of 0.1. (2 points).

10. Find the value of the coefficient of determination (2 ways, 4 points).

11. Interpret the value of R²found in the previous question (2 points).

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

Answer 1