What is the relationship between the linear correlation coefficient r and the slope of a regression line?

The relationship is that the value of the linear correlation coefficient will always have the same sign as the value of the slope of a regression line.

Step-by-step explanation:

The slope of regression is simply the covariance between X and Y divided by the variance of X i.e Cov(X, Y)/Var X. Whereas, the correlation is the covariance divided by the product of the standard deviation. Thus, we can say that the correlation is the product of the gradient of the regression line and the ratio of the standard deviations.

Thus, it means when the correlation is positive, the slope is also positive and vice versa.

The sign of the correlation coefficient, r, is always the same as that of the slope of the regression line.

Therefore, the sign of the correlation coefficient, r, is always the same as that of the slope of the regression line.

Learn more about correlation coefficient on:

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options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2