Question

graph the line of best fit for each set of points listed below. (3,4) (7,6)(-2,-4)
determine whether the points in each scatter - plot have a positive correlation, a negative correlation, or no correlation. then, determine which r - value is most accurate.
a r = 0.07
b r = 0.7
c r = 0.83
d r = 1
write the equation for the line of best fit for each set of points listed below. (use desmos) (-8,7) (-5,3) (3,6) (9,0)
f(x)=____
predict what the function equals when f(5).
f(5)=____
determine whether the points in each scatter - plot have a positive correlation, a negative correlation, or no correlation. then, determine which r - value is most accurate.
a r = 0.9
b r=-0.6
c r = 0.02
d r = 0.006

Explanation:

Step1: Recall correlation concept

Positive correlation means as one variable increases, the other increases. Negative correlation means as one variable increases, the other decreases. No - correlation means no linear relationship.

Step2: Analyze first scatter - plot

In the first scatter - plot on the right, as the x - values increase, the y - values generally increase. So, it has a positive correlation. The r - value for a strong positive correlation is close to 1. Among the options A. $r = 0.07$, B. $r=0.7$, C. $r = 0.83$, D. $r = 1$, the most accurate r - value for a positive correlation with some scatter is C. $r = 0.83$.

Step3: Analyze second scatter - plot

In the second scatter - plot on the right, there is no clear pattern of increase or decrease as x changes. So, it has no correlation. The r - value closest to 0 indicates no correlation. Among the options A. $r=-0.9$, B. $r = - 0.6$, C. $r = 0.02$, D. $r = 0.006$, the most accurate r - value is C. $r = 0.02$.

Step4: Find line of best - fit equation

For the points $(-8,7),(-5,3),(3,6),(9,0)$, using a linear regression formula (or a tool like Desmos), the general form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. After calculation (using the least - squares method or a graphing utility), the equation of the line of best - fit is $F(x)=-\frac{1}{2}x+\frac{3}{2}$.

Step5: Evaluate the function

To find $F(5)$, substitute $x = 5$ into $F(x)=-\frac{1}{2}x+\frac{3}{2}$. Then $F(5)=-\frac{1}{2}\times5+\frac{3}{2}=\frac{-5 + 3}{2}=-1$.

Answer:

1. C. $r = 0.83$
2. C. $r = 0.02$
3. $F(x)=-\frac{1}{2}x+\frac{3}{2}$
4. $F(5)=-1$