What is the significance of a correlation coefficient of
−0. 97?
a. The points all lie very close to the line of fit, and the
line is decreasing.
b. The points all lie very close to the line of fit, and the
line is increasing.
c. The points do not follow the line of fit and, the line is
decreasing.
d. The points do not follow the line of fit, and the line is
increasing
d. The points do not follow the line of fit, and the line is increasing
The correct option is: c. The points do not follow the line of fit, and the line is decreasing.
A correlation coefficient of -0.97 indicates a strong negative correlation between the two variables. The negative sign indicates a decreasing relationship, meaning that as one variable increases, the other variable tends to decrease. The value -0.97 indicates a strong correlation, meaning that the points do not deviate much from the line of fit.
To understand the significance of a correlation coefficient of -0.97, we need to understand what a correlation coefficient represents. The correlation coefficient, often denoted as r, measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative linear relationship, +1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.
In this case, a correlation coefficient of -0.97 signifies a very strong negative linear relationship between the variables being analyzed. It means that as one variable increases, the other variable tends to decrease, and vice versa. The closer the correlation coefficient is to -1 or +1, the stronger the linear relationship.
Given the options provided, the correct answer would be:
c. The points do not follow the line of fit, and the line is decreasing.
Explanation: A correlation coefficient of -0.97 indicates that the points do not closely follow the line of fit since the relationship between the variables is negative. When the line is decreasing, it means that one variable decreases as the other variable increases, which is consistent with a negative correlation. Therefore, option c is the best representation of the significance of a negative correlation coefficient of -0.97.
is it a or c
Apologies for the confusion. The correct answer is:
a. The points all lie very close to the line of fit, and the line is decreasing.
A correlation coefficient of -0.97 indicates a strong negative linear relationship between the variables. The points in the scatterplot closely follow the line of fit, indicating that the relationship is highly consistent. Additionally, the negative sign indicates that as one variable increases, the other variable tends to decrease. The line of fit is decreasing, indicating the direction of the relationship. So, option a is the correct answer.