Question

The slope of a regression line based on sample data and the calculated correlation coefficient using the same sample data ____________.

	A.	will have the same sign
	B.	are equal in value
	C.	are equal to the half of the slope and has the opposite sign
	D.	are equal in magnitude and have opposite signs

Answer 1

The relationship between slope of regression line and correlation coefficient is as follows -

We know that & are standard deviation of x & y respectively which cannot be negative values.

So, sign of slope of regression line only depends on sign of correlation coefficient. Hence, if the correlation coefficient is positive then regression coefficient is also positive or vice-versa.

This means that slope of regression line & correlation coefficient will have the same sign.

Hence, option A is correct.

From the formula, we can see that regression coefficient & correlation coefficient can't be equal or different in signs. Also, correlation coefficient are not half of the slope & has opposite sign.

So, other options are incorrect.

answered by: anonymous

Answer 2

The regression line is given by the equation ,

Y= aX + b

Where, a= the slope of regression line.

b= y- intercept of the line.

Now, the slope of a line is the chance in the value of dependent variable Y by one unit change in the value of independent variable X, and it is given by the formula,

Slope , a = r ( sy/ sx )

Where, r= sample correlation coefficient.

Sx and Sy are the sample standard deviations of x and y respectively.

Since, the value of standard deviations can't be negative.

So, The slope (a) and sample correlation coefficient (r) will have the same sign.

answered by: Mavic