How to interpret if coefficient of specification is 0 (zero)? a) There is no relationship between the dependent variable and the independent variable

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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How to interpret if coefficient of specification is 0 (zero)?
a)
There is no relationship between the dependent variable and the independent variable.

B)
There is no relationship between the dependent variable and the independent variable

NS)
No comment can be made as the correlation coefficient is not given

D)
The independent variable does not explain the dependent variable at all.

TO)
The coefficient of designation cannot theoretically be 0 (zero)

Expert Solution
Step 1

The coefficient of specification is nothing but the slope coefficient b1 in a regression line. 

Let y= a+ bx be the regression line. 

Here, a is the intercept, b is the slope, x is the  independent variable and y is the independent variable. 

The coefficient of the specification is nothing but the slope coefficient 

If the slope of the coefficient b1 is positive, then there is a positive linear relationship between independent variable and the dependent variable. That is, if one increases, the other increases.

If the slope of the coefficient b1 is negative, then there is a negative linear relationship between the independent variable and the dependent variable.

That is, if one increases the other variable decreases.

If the slope coefficient  is 0, then as one increases, the other remains constant. That is, there is no predictive relationship. In other words, there is no relationship between the independent variable and the dependent variable. 

 

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