Answered: What do we mean when we say that a multiple regression model is a multiple linear regression model? What does "linear" mean here? Can we allow any "higher-order...

MATLAB: An Introduction with Applications

6th Edition

ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

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What do we mean when we say that a multiple regression model is a multiple linear regression model? What does "linear" mean here? Can we allow any "higher-order terms"? Explain.

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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The multiple linear regression model is a statistical technique which is used to predict a response variable based on the several explanatory variable. This model is said to be linear when there is a linear relationship is between the response variable and the explanatory variables.

The first order multiple linear regression model is,

$y = β_{0} + β_{1} x_{1} + β_{2} x_{2} + . . . + β_{k} x_{k}$

Where, $β_{0}$ is the mean of the y when all the predictor variables equal to 0.

$β_{1}, β_{2}, . . ., β_{k}$ are said to be slope of the line relative y to $x_{1}, x_{2, . . .,} x_{k}$

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What do we mean when we say that a multiple regression model is a multiple linear regression model? What does "linear" mean here? Can we allow any "higher-order terms"?

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