Question

a scatter plot, line of best fit and a regression analysis is shown for a linear regression fit to model the data.
$y_1sim mx_1 + b$
statistics
$r^{2}=0.9504$
$r = - 0.9749$
residuals
$c_1$ plot
parameters
$m=-1.14798$
$r = 8.98548$
which of the following statements are true? select all that apply.
the correlation coefficient is 0.9504.
the correlation coefficient is - 0.9749.
the equation for the line of best fit is $y=-0.0749x + 0.9504$.
the equation for the line of best fit is $y=-1.14798x + 8.98548$.
the correlation coefficient demonstrates a strong, negative, linear association.
the correlation coefficient demonstrates a strong, positive, linear association.

Explanation:

Step1: Identify correlation coefficient

The correlation coefficient is denoted by $r$. From the given statistics, $r=- 0.9749$. So the statement "The correlation coefficient is -0.9749" is true and "The correlation coefficient is 0.9504" is false.

Step2: Identify line - of - best - fit equation

The equation of a line of best - fit is in the form $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given $m=-1.14798$ and $b = 8.98548$, the equation of the line of best - fit is $y=-1.14798x + 8.98548$. So the statement "The equation for the line of best fit is $y=-1.14798x + 8.98548$" is true and "The equation for the line of best fit is $y=-0.0749x + 0.9504$" is false.

Step3: Analyze the correlation

Since $r=-0.9749$ and $|r|\approx1$, it indicates a strong linear association. The negative sign of $r$ means it is a negative linear association. So the statement "The correlation coefficient demonstrates a strong, negative, linear association" is true and "The correlation coefficient demonstrates a strong, positive, linear association" is false.

Answer:

The correlation coefficient is -0.9749.
The equation for the line of best fit is $y=-1.14798x + 8.98548$.
The correlation coefficient demonstrates a strong, negative, linear association.