a.Calculate and interpret a 95 ⁢ % CI for the population regression coefficient on x1b. The estimated standard deviation of the predicted y when x1 = 400 and x2 = .125 is .180 . Calculate a 95 ⁢ % CI for true average roughness under these circumstances. The article "Optimization of Surface Roughness in Drilling Using Vegetable-Based Cutting Oils Developed from Sunflower Oil" (Industrial Lubrication andTribology, 2011: 271-276) gave the following data on ₁ = spindle speed (rpm),T₂ = feed rate (mm/rev), z3 = drilling depth (mm), and y = surface roughness (μm)when a semisynthetic cutting fluid was used:IL32032032042042042052052052022.10.12.14.10.12.14.10.12.1413152025202515251520y2.274.144.691.922.634.342.032.342.67-1.321.080.26-0.40-0.790.991.640.03-1.52

x1 x2 x3 y e* 320 0.1 15 2.27 1.32 320 0.12 20 4.14 1.08 320 0.14 25 4.69 0.26 420 0.1 20…

.Calculate and interpret a 95 ⁢ % CI for the population regression coefficient on x1 b. The estimated standard deviation of the predicted y when x1 = 400 and x2 = .125 is .180 . Calculate a 95 ⁢ % CI for true average roughness under these circumstances

.Calculate and interpret a 95 ⁢ % CI for the population regression coefficient on x1 b. The estimated standard deviation of the predicted y when x1 = 400 and x2 = .125 is .180 . Calculate a 95 ⁢ % CI for true average roughness under these circumstances

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

a.Calculate and interpret a 95 ⁢ % CI for the population regression coefficient on x1

b. The estimated standard deviation of the predicted y when x1 = 400 and x2 = .125 is .180 . Calculate a 95 ⁢ % CI for true average roughness under these circumstances.

The article "Optimization of Surface Roughness in Drilling Using Vegetable-
Based Cutting Oils Developed from Sunflower Oil" (Industrial Lubrication and
Tribology, 2011: 271-276) gave the following data on ₁ = spindle speed (rpm),
T₂ = feed rate (mm/rev), z3 = drilling depth (mm), and y = surface roughness (μm)
when a semisynthetic cutting fluid was used:
IL
320
320
320
420
420
420
520
520
520
22
.10
.12
.14
.10
.12
.14
.10
.12
.14
13
15
20
25
20
25
15
25
15
20
y
2.27
4.14
4.69
1.92
2.63
4.34
2.03
2.34
2.67
-1.32
1.08
0.26
-0.40
-0.79
0.99
1.64
0.03
-1.52

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Step 5: Calculate a 95% CI for true average roughness under the given circumstances.

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