How do I prove that it does pass through (mean x, mean y) 2.89 A property of the least-squares regressionline. Use the equation for the least-squares regressionline to show that this line always passes through thepoint (x, y).

Name: How do I prove that it does pass through (mean x, mean y) 2.89 A prope
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Description: How do I prove that it does pass through (mean x, mean y) 2.89 A property of the least-squares regressionline. Use the equation for the least-squares regressionline to show that this line always passes through thepoint (x, y).

Answered: 2.89 A property of the least-squares…

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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How do I prove that it does pass through (mean x, mean y)

2.89 A property of the least-squares regression
line. Use the equation for the least-squares regression
line to show that this line always passes through the
point (x, y).

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 + ...

Expert Solution

Step 1

Suppose we are given a straight line

y=a+bx

, then we say that the line passes through the point (x₀, y₀ ), if and only if:

a+bx₀ = y₀ is satisfied.

In our case, we need to show that the line of regression always passes through ( $x, y$ ),

First recall the equation of least squares is given by:

y- $y$ = $\frac{c o v (x, y)}{{σ_{x}}^{2}}$ (x- $x$ ), where cov(x,y) is the covariance between X and Y, and ${σ_{x}}^{2}$ is the variance of X

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