Answered: In linear regression analysis, the…

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

In linear regression analysis, the coefficient for the x-variable when the y-variable is regressed on the x-variable can be thought of as:

Note: more than one answer may be correct

Group of answer choices

How much the value of the predicted y-variable will change when the x-variable changes by one unit.

In the simple (two variable) linear regression model, the coefficient can be thought as the slope coefficient that measures the responsiveness of y to changes in x.

The estimated coefficient will change if the sample containing x and y changes.

The sample coefficient is an estimate of the population coefficient

Before interpreting the coefficient for the x-variable, we should test whether the coefficient is statistically significant.

Expert Solution

Step 1: Introduction to the given problem

Given that, the y-variable is regressed to the x-variable.

We can write the least square regression equation as,

$y with hat on top equals a plus b asterisk times x space space space space space space space space space space space space space space space space space space space W h e r e comma space a space equals space I n t e r c e p t space a n d space b space equals space S l o p e space$

y is the dependent variable and x is the independent variable

We are asked to interpret the slope (coefficient of x-variable)