Question

which statements are true regarding the data in the table? select all that apply.

x	y
-8	1
-6	10
0	-6
3	-3
10	0

• the correlation coefficient is 0.19.
• the correlation coefficient is -0.44.
• there is a strong linear association between the variables.
• the slope of the regression line that models this data is negative.
• there is a weak linear association between the variables.

Explanation:

Step1: Calculate the correlation coefficient

Using a calculator or software (e.g., Excel's CORREL function) with the \(x\) and \(y\) values \((-8,1),(-6,10),(0, - 6),(3,-3),(10,0)\), we find the correlation coefficient \(r\approx - 0.44\).

Step2: Analyze the slope of the regression line

Since the correlation coefficient \(r=-0.44<0\), the slope of the regression line (which has the same sign as \(r\) for linear regression) is negative.

Step3: Determine the strength of the linear association

The value of \(|r| = 0.44\). Since \(0.3<|r|<0.7\), there is a weak linear association.

Answer:

The correlation coefficient is - 0.44, The slope of the regression line that models this data is negative, There is a weak linear association between the variables.