Question

When doing regression, simple linear or any of the other regression approaches, the analyst always must begin with the determination/isolation of at least two key variables -- one "dependent" and the other "independent". So, for example, I may do a forecast of future profits that relies on sales data (independent) and associated profit data (dependent) from the same years. We say something like...

"Since profits "depend" on sales volume (not the other way around), we can use one (sales) to forecast the other (profit)."

Find an example of a regression model with Google. Then explain which variables used in the model are "dependent" vs. "independent."

Answer 1

The linear relationship between two variables is representated by a straight line which is known as Regression line.

The line of regression Y on X is

Y = a + bX.

Where Y is response variable (dependent variable) and X is independent variable.

And a -Y intercept and b is slope of line.

example :

Exam scores depends on I.Q.

Exam score : dependent variable and I.Q. : Independent variables.

Numerical Example:

The I.Q's of a group of 6 persons were measured and then they were made to appear in a certain examination. TheirI.Q's and examination scores were as follows.

Person	1	2	3	4	5	6
I.Q.	110	100	140	120	80	90
Exam Score	70	90	80	60	10	20

By using R

> x=c(110,100,140,120,80,90)
> y=c(70,90,80,60,10,20)
> l=lm(y~x)
> l

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept) x  
-59.286 1.071  

From output

The regression line Y (Exam score) on X (I.Q ) is

Y = 59.286 + 1.071 X