Least Squares Linear Regression of Sweet Index on Statistix Software Worksheet

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Mathematics

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Exercises marked with PO Required require the use of Statistix 10.0 software.

The files required to solve for PO using SX: https://wetransfer.com/downloads/02b84789d90488d46b903df6008a05b820201012100139/23e15fb9419565fbbd9458f2550e082f20201012100200/898d57

The Problems: https://wetransfer.com/downloads/86138aeaaed70f3f1b6e6a5ab19b887920201012110122/71ed6c33efbdc663560fd7802fc675e720201012110150/a4b178

Orange Juice Problems (OJUICE data)

11.26 a, b, c (632) // PO Required: SLR result

11.42 a, b, c (639) // PO Required: OK to include SLR result from 11.26

11.54 (646) // PO Required: OK to include SLR result from 11.26

11.77 (656) // PO Required: OK to include SLR result from 11.26 AND correlation table

11.89 (664) // PO Required: NONE

Non-Orange Juice Problems

11.52 a, b, c (645) // PO Required: NONE

12.9 a, b, c, d (698) // PO Required: NONE

12.33 a, b, c, d, e (709) -- TEAMPERF data // PO Required: MLR result AND prediction/fitted interval result

12.38 a, b, c (714) // PO Required: NONE

Question 10: What is one thing that you plan to change about your study habits following our first exam? // PO Required: NONE

Submit a Word file (named HW2YourName) with your answers (include SX printouts where required).

Exercises marked with PO Required require the use of Statistix 10.0 software.

Unformatted Attachment Preview

11.26 Sweetness of orange juice. The quality of the orange juice produced by a manufacturer (e.g., Minute Maid, Tropicana) 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 24 production runs at a juice manufacturing plant are shown in the table below. Suppose a manufacturer wants to use simple linear regression to predict the sweetness ) from the amount of pectin (). Run Sweetness Index Pectin (ppm) 1 5.2 220 2 5.5 227 3 6.0 259 4 5.9 210 5 5.8 224 6 6.0 215 7 5.8 231 8 5.6 268 9 5.6 239 10 5.9 212 11 5.4 410 12 5.6 256 13 5.8 306 14 5.5 259 5.3 284 16 5.3 383 17 5.7 271 18 5.5 264 19 5.7 227 20 5.3 263 21 5.9 232 22 5.8 220 23 5.8 246 24 5.9 241 Note: The data in the table are authentic. For confidentiality reasons, the manufacturer cannot be disclosed. a. Find the least squares line for the data. b. Interpret B, and ß in the words of the problem. c. Predict the sweetness index if amount of pectin in the orange juice is 300 ppm. [Note: A measure of reliability of such a prediction is discussed in Section 11.60] 11.42 Sweetness of orange juice. Refer to the study of the quality of orange juice produced at a juice manufacturing plant, Exercise 11.26 (p. 632). Recall that simple linear regression was used to predict the sweetness index (Y) from the amount of pectin (x) in the orange juice. a. Find the values of SSE, 82, and s for this regression. b. Explain why it is difficult to give a practical interpretation to sa. c. Give a practical interpretation of the value of s. 11.54 Sweetness of orange juice. Refer to the simple linear regression relating y = sweetness index of an orange juice sample with x = amount of water-soluble pectin, Exercise 11.26 (p. 632). Use the results of the regression to form a 95% confidence interval for the slope, B1. Interpret the result.
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Explanation & Answer

Hi, everything is done: here is the problem solutions with outputs and the zip file of outputs

Problem: 11.26:
Part A:
Output:
Statistix 10.0 (30-day Trial)
PM

OJUICE.sx, 10/15/2020, 1:01:50

Least Squares Linear Regression of SweetInde
Predictor
Variables
Constant
Pectin

Coefficient
6.25207
-2.311E-03


Adjusted R²
AICc
PRESS

0.2286
0.1936
-68.670
1.1714

Std Error
0.23662
9.049E-04

T
26.42
-2.55

P
0.0000
0.0181

Mean Square Error (MSE)
Standard Deviation

0.04622
0.21500

Source
Regression
Residual
Total

DF
1
22
23

SS
0.30140
1.01693
1.31833

MS
0.30140
0.04622

F
6.52

P
0.0181

Lack of Fit
Pure Error

19
3

0.69193
0.32500

0.03642
0.10833

0.34

0.9424

Cases Included 24

Missing Cases 0

Hence, the least squares line for the data is, Sweetness Index = 6.25 -0.00231Pectin (ppm).

Part B: The value of represents the 0.0023 units decrease in sweetness Index with one unit
increase in Pectin (ppm).
Part C:
The regression line is Substitute 300 for Pectin in the regression equation.
Hence we have:
Sweetness Index = 6.25 -0.00231Pectin (ppm)
=6.25-(0.00231x300)
= 5.557

Problem: 11.42:
Output:
Statistix 10.0 (30-day Trial)
PM

OJUICE.sx, 10/15/2020, 1:01:50

Least Squares Linear Regression of ...


Anonymous
Really helpful material, saved me a great deal of time.

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