Question

Which of the following statements concerning the linear correlation coefficient are​ true? ​I: If the linear correlation coefficient for two variables is​ zero, then there is no relationship between the variables. ​II: If the slope of the regression line is​ negative, then the linear correlation coefficient is negative. ​III: The value of the linear correlation coefficient always lies betweenminus1 and 1. ​IV: A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of minus0.82.

Answer 1

Answer:

​I: If the linear correlation coefficient for two variables is​ zero, then there is no relationship between the variables. ​II: If the slope of the regression line is​ negative, then the linear correlation coefficient is negative. ​III: The value of the linear correlation coefficient always lies between minus 1 and 1. ​

Step-by-step explanation:

A correlation coefficient is a measure of how closely the variables are related.  This coefficient ranges from -1 to 1, with -1 being a perfect fit for a decreasing data set and 1 being a perfect fit for an increasing data set.

If the data set has a negative correlation coefficient, the data is decreasing; this means that the slope of the regression line will be negative.

The closer the correlation coefficient is to -1 or 1, the better the fit; this means that a correlation coefficient of -0.82 will be stronger than one of 0.62.