Computer a 95 % confidence interval for the mean prediction when the true roughness is 0.8 um An article presents the results of an experiment in which the surface roughness (in μm) was measured for 15 D2 steelspecimens and compared with the roughness predicted by a neural network model. The results are presented in thefollowing table.TRUE Value (x)Predicted Value (y)Check my work0.450.4000.820.70.540.520.410.390.770.740.790.780.250.270.620.60.910.870.520.511.020.910.60.710.580.50.870.911.061.04To check the accuracy of the prediction method, the linear model y= Bo+B1x+ & is fit. If the prediction method isaccurate, the value of ẞo will be 0 and the value of ẞ1 will be 1.Note: This problem has a reduced data set for ease of performing the calculations required. This differs from the dataset given for this problem in the text.

The predicted value (y) is given.Want to calculate a 95% confidence interval for the mean…

Answered: An article presents the results of an…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Computer a 95 % confidence interval for the mean prediction when the true roughness is 0.8 um

An article presents the results of an experiment in which the surface roughness (in μm) was measured for 15 D2 steel
specimens and compared with the roughness predicted by a neural network model. The results are presented in the
following table.
TRUE Value (x)
Predicted Value (y)
Check my work
0.45
0.400
0.82
0.7
0.54
0.52
0.41
0.39
0.77
0.74
0.79
0.78
0.25
0.27
0.62
0.6
0.91
0.87
0.52
0.51
1.02
0.91
0.6
0.71
0.58
0.5
0.87
0.91
1.06
1.04
To check the accuracy of the prediction method, the linear model y= Bo+B1x+ & is fit. If the prediction method is
accurate, the value of ẞo will be 0 and the value of ẞ1 will be 1.
Note: This problem has a reduced data set for ease of performing the calculations required. This differs from the data
set given for this problem in the text.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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