Answered: On linear regression: Part a. Which…

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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On linear regression:

Part a.

Which of the following are standard assumptions of a linear regression model (check all that apply) :

The predictor and response variable are both normally distributed.

The residuals are all equal to zero.

The relationship between the predictor and response variable is linear.

The residuals have an approximately normal distribution.

A line describes all of the predictable relationship between the predictor and response variables.

part B:

Which of the following are assumptions made about the errors in a simple linear regression model? (check all that apply):

Observations from a uniform distribution

Distribution has standard deviation = 1

Dependent observations

Independent observations

Observations from a normal distribution

Distribution has constant standard deviation

Distribution has mean = zero

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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Assumptions for the linear regression model and the errors in the simple linear regression model.

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