Question

given the regression equation for a particular correlation is y = 0.44x - 15. which of the following statements is/are correct?

a. correlation coefficient(r) is positive

b. slope is 15

c. variance in the data is positive

d. slope is -0.44

e. r^2 is positive

Explanation:

Step1: Analyze the regression - equation form

The regression equation is in the form $Y = mx + b$, where $m$ is the slope. For the equation $Y = 0.44x-15$, the slope $m = 0.44$.

Step2: Understand the relationship between slope and correlation coefficient

The sign of the slope of the regression line is the same as the sign of the correlation coefficient $r$. Since the slope $m = 0.44>0$, the correlation coefficient $r$ is positive.

Step3: Recall properties of variance and $r^2$

The variance of a non - constant data set is always positive. Also, $r^{2}$ (the coefficient of determination) is non - negative. In a non - trivial regression (where there is some linear relationship), $r^{2}>0$.

Answer:

a. Correlation coefficient(r) is positive
c. Variance in the data is positive
e. $r^2$ is positive