Question

In a simple regression analysis (where y is a dependent and x an independent variable), if the y-intercept is positive, then it must be true that _____.

Answer 1

Answer:

$m=\frac{S_{xy}}{S_{xx}}$  

Where:  

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$  

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$  

$\bar x= \frac{\sum x_i}{n}$  

$\bar y= \frac{\sum y_i}{n}$  

And we can find the intercept using this:  

$b=\bar y -m \bar x$  

On this case the correct answer would be:

E.  none of the above

Since the intercept has no association between the increase/decrease of the dependent variable respect to the independent variable

Step-by-step explanation:

Assuming the following options:

A.  there is a positive correlation between X and Y

B.  there is a negative correlation between X and Y

C.  if X is increased, Y must also increase

D.  if Y is increased, X must also increase

E.  none of the above

If we want a model $y = mx +b$ where m represent the lope and b the intercept

$m=\frac{S_{xy}}{S_{xx}}$  

Where:  

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$  

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$  

$\bar x= \frac{\sum x_i}{n}$  

$\bar y= \frac{\sum y_i}{n}$  

And we can find the intercept using this:  

$b=\bar y -m \bar x$  

On this case the correct answer would be:

E.  none of the above

Since the intercept has no association between the increase/decrease of the dependent variable respect to the independent variable