Final answer:
The statement that a high negative correlation indicates a strong inverse relationship between two variables is true. The correlation coefficient reflects the strength and direction of this relationship. Variables with strong negative correlations are good candidates for linear regression analysis.
Step-by-step explanation:
True or False: A high negative correlation indicates that the variables are strongly related in an inverse fashion. This statement is true. A negative correlation means that the variables move in opposite directions. For example, if one variable increases, the other tends to decrease, and vice versa. The further away the correlation coefficient is from zero, whether it is positive or negative, the stronger the relationship between the variables. A correlation coefficient of -0.9 indicates a stronger relationship than a correlation coefficient of -0.5. Therefore, options a (True) and a (-0.90) suggest strong negative relationships.
The correlation coefficient indicates the weakest relationship when it is closest to 0. Variables with a strong negative linear relationship, such as a correlation coefficient of -0.9, would be good candidates for analysis with linear regression because the relationship between the variables is predictable and strong.
It is important to note that correlation does not imply causation. A strong correlation, whether positive or negative, does not mean that one variable causes the other to change. It simply indicates a consistent and predictable association between the two variables.