1. Write down the multiple regression function?2. What is the multiple correlation and the multiple standard error of estimate?3. What is the coefficient of multiple determination and what does it mean?4. Of the three independent variables, which independent variable is not significant as a predictor (α = 0.05)? Model SummaryAdjusted RSquare.493Std. Error ofModelRR Squarethe Estimate1.723*.523.29043a. Predictors: (Constant), X3, X1, X2ANOVASum ofModelSquaresdfMean SquareFSig.1Regression4.44331.48117.559.000Residual4.04948.084Total8.49251a. Dependent Variable: X4b. Predictors: (Constant), X3, X1, X2CoefficlentsStandardizedCoefficientsUnstandardized CoefficientsBStd. ErrorBetaSig.Model1(Constant)1.210.4312.808.007X1.294.125.3412.341.023X2.086.126.102.679.500X3329.1303662.526015a. Dependent Variable: X4

From the output, the constant value is 1.210.

Answered: 1. Write down the multiple regression…

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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Question

1. Write down the multiple regression function?
2. What is the multiple correlation and the multiple standard error of estimate?
3. What is the coefficient of multiple determination and what does it mean?
4. Of the three independent variables, which independent variable is not significant as a predictor (α = 0.05)?

Model Summary
Adjusted R
Square
.493
Std. Error of
Model
R
R Square
the Estimate
1
.723*
.523
.29043
a. Predictors: (Constant), X3, X1, X2
ANOVA
Sum of
Model
Squares
df
Mean Square
F
Sig.
1
Regression
4.443
3
1.481
17.559
.000
Residual
4.049
48
.084
Total
8.492
51
a. Dependent Variable: X4
b. Predictors: (Constant), X3, X1, X2
Coefficlents
Standardized
Coefficients
Unstandardized Coefficients
B
Std. Error
Beta
Sig.
Model
1
(Constant)
1.210
.431
2.808
.007
X1
.294
.125
.341
2.341
.023
X2
.086
.126
.102
.679
.500
X3
329
.130
366
2.526
015
a. Dependent Variable: X4

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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