Exam 17: Correlation

In order to find the correlation coefficient, the estimated least-squares regression line is always found first.

If the hypothesis that $Q=0$ is rejected, then

The hypothesis of no correlation between two variables can always be rejected if $r$ is greater than zero.

The variables circulation $\left(x_{1}\right)$ and advertising income $\left(x_{2}\right)$ are used to predict the annual profit of a daily newspaper ( $y$ ). A multiple correlation coefficient of 0.65 is obtained. For predicting annual profit on the basis of advertising income alone, a value of $r=0.78$ is found. Comment on these results.

The value $r^{2}$ can assume any value between __________.

If a regression line is horizontal, then the correlation between the two variables is __________.

It is never possible for $\sum(\hat{y}-\bar{y})^{2}$ to exceed $\sum(y-\bar{y})^{2}$ .

A high correlation between two variables will not prove that one variable causes the other to occur.