Answer:
Carrie's slope value is correct.
Step-by-step explanation:
The least square regression line is: [tex](y -\bar y)=b_{yx} (x-\bar x)[/tex]
Here [tex]b_{yx}[/tex] is the slope of the line.
The formula to compute the slope is:
[tex]b_{yx}=r\frac{\sigma_{x}}{\sigma_{y}}[/tex]
Here [tex]\sigma_{x}[/tex] = standard deviation of x and [tex]\sigma_{y}[/tex] = standard deviation of y.
It is provided that the standard deviation of x and y are equal.
So the slope of the regression line is:
[tex]b_{yx}=r\frac{\sigma_{x}}{\sigma_{y}}=r\frac{\sigma_{x}}{\sigma_{x}}=r[/tex]
Thus, if the standard deviation of x and y are equal the slope of the line is same as the correlation coefficient.
The correlation coefficient is a measure used to determine the strength of the linear relationship between the variables.
It ranges from -1 to 1.
Carrie's slope value was 0.50 and Ryan's slope value was 2.
Since -1 ≤ r ≤ 1 the value of slope cannot be 2.
Thus, Ryan's slope value is incorrect.
