A computer was used to compare the x and y values of points in a data set the scatter plot of the data and the information generated by the computer about the line of best fit are shown what is the correlation coefficient of the data

Question

Y=ax+b
A=-1.28
B=1.022
R^2=0.569
R=-0.745

Answer 1

The correlation coefficient (R) indicates the strength and direction of the linear relationship between two variables. In your provided information, you have:

• \( R^2 = 0.569 \)
• \( R = -0.745 \)

The correlation coefficient \( R \) is already given as -0.745. This value suggests a moderate to strong negative correlation between the x and y values in your data set.

If you are looking for confirmation or an explanation about the significance of these values:

• \( R^2 \) (the coefficient of determination) measures how well the line of best fit explains the variation of the data; in this case, about 56.9% of the variance in y can be explained by the linear relationship with x.
• The negative sign of \( R \) indicates that as x increases, y tends to decrease.

So, the correlation coefficient of the data is \( R = -0.745 \).