Question

Bella recorded data and used her graphing calculator to find the equation for the line of best fit. She then used the.correlation coefficient to determine the strength of the linear fit. Which correlation coefficient represents the strongest linear relationship?

0.9 -0.3
0.5 -0.8

Answer 1

Answer: The correlation coefficient (also known as Pearson's correlation coefficient or r) is a measure of the strength of the linear relationship between two variables. The value of the correlation coefficient ranges between -1 and 1, with a value of 1 indicating a perfect positive linear relationship, a value of -1 indicating a perfect negative linear relationship, and a value of 0 indicating no linear relationship.

In this case, the correlation coefficient that represents the strongest linear relationship is

0.9

The absolute value of the correlation coefficient measures the strength of the linear relationship, regardless of whether it is positive or negative. So, the absolute value of 0.9 and -0.3 are both 0.9. but as we are looking for the strongest linear relationship, the value of 0.9 is closer to 1 than -0.3 is and it indicates stronger positive relationship.

In summary, the closer the correlation coefficient is to 1 or -1, the stronger the linear relationship between the variables is. In this case, 0.9 has the strongest linear relationship of the given options.

Step-by-step explanation:

Answer 2

The correlation coefficient 0.9 represents the strongest linear relationship among the given options because its magnitude is closest to 1, regardless of its positive sign.

Step-by-step explanation:

The correlation coefficient is a statistical measure that calculates the strength of the relationship between the relative movements of two variables. The values range between -1.0 and 1.0. A correlation of 1.0 shows a perfect positive correlation, while a correlation of -1.0 shows a perfect negative correlation. A correlation of 0.0 shows no relationship between the movement of the variables.

Given the options of 0.9, -0.3, 0.5, and -0.8, the value 0.9 indicates the strongest linear relationship because its magnitude is closest to 1. It doesn't matter whether the correlation is positive or negative when we are only considering its strength; the sign indicates the direction of the relationship, not the strength. Thus, -.90 would also represent a very strong relationship, albeit negative. The correlation coefficients which are farthest from zero in either the positive or negative direction indicate the strongest linear relationship.