Question

a scatter plot, line of best fit and a regression analysis is shown for a linear equation fit to model the data.

$y_1\sim mx_1 + b$

statistics
$r^{2}=0.9042$
$r = 0.9509$

residuals
$e_1$ plot

parameters
$m = 1.36552$
$r=-0.887903$

which of the following statements are true? select all that apply

the correlation coefficient is 0.9509
the correlation coefficient is 0.9042
the equation for the line of best fit is $y = 0.9509x-0.887903$
the equation for the line of best fit is $y = 1.36552x-0.887903$
the correlation coefficient demonstrates a strong, negative, linear association
the correlation coefficient demonstrates a strong, positive, linear association

Explanation:

Step1: Recall correlation - coefficient notation

The correlation coefficient is denoted by $r$. From the given statistics, $r = 0.9509$. So the statement "The correlation coefficient is 0.9509" is true.

Step2: Recall coefficient - of - determination notation

The coefficient of determination is denoted by $r^{2}$. Here $r^{2}=0.9042$, but the question asks about the correlation coefficient, not the coefficient of determination. So the statement "The correlation coefficient is 0.9042" is false.

Step3: Recall the form of the line - of - best - fit equation

The equation of a line of best - fit is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given $m = 1.36552$ and $b=-0.887903$, the equation of the line of best - fit is $y = 1.36552x-0.887903$. So the statement "The equation for the line of best - fit is $y = 0.9509x-0.887903$" is false and the statement "The equation for the line of best - fit is $y = 1.36552x-0.887903$" is true.

Step4: Analyze the sign of the correlation coefficient

Since $r = 0.9509>0$, it represents a strong, positive, linear association. So the statement "The correlation coefficient demonstrates a strong, negative, linear association" is false and the statement "The correlation coefficient demonstrates a strong, positive, linear association" is true.

Answer:

The correlation coefficient is 0.9509.
The equation for the line of best - fit is $y = 1.36552x-0.887903$.
The correlation coefficient demonstrates a strong, positive, linear association.