A coach is assessing the correlation between the number of hours spent practicing and the average number of points scored in a game. The table below shows the data: Number of hours spent practicing (x) 0 0.5 1 1.5 2 2.5 3 3.5 4 Score in the game (y) 5 8 11 14 17 20 23 26 29 Part A: Is there any correlation between the number of hours spent practicing and the score in the game?Justify your answer. (4 points) Part B: Write a function which best fits the data. (3 points) Part C: What does the slope and y-intercept of the plot indicate? (3 points)

a)  

We have a perfect linear relationship between the two variables

b)  

Nowe we can find the means for x and y like this:  

And we can find the intercept using this:  

So the line would be given by:  

c) For this case the slope indicates that for each increase of the number of hours in 1 unit we have an expected increase in the score about 6 units.

And the intercept 5 represent the minimum score expected for any game

Step-by-step explanation:

We have the following data:

Number of hours spent practicing (x) 0 0.5 1 1.5 2 2.5 3 3.5 4

Score in the game (y) 5 8 11 14 17 20 23 26 29

Part a

The correlation coefficient is given:

For our case we have this:

n=9  

We have a perfect linear relationship between the two variables

Part b

Where:  

With these we can find the sums:  

And the slope would be:  

Nowe we can find the means for x and y like this:  

And we can find the intercept using this:  

So the line would be given by:  

Part c

For this case the slope indicates that for each increase of the number of hours in 1 unit we have an expected increase in the score about 6 units.

And the intercept 5 represent the minimum score expected for any game

i leave the calculator work to you.

7. diameter 4 miles, circumference 4π miles

8. radius 0.2 miles, circumference 0.4π miles

[this is a bad problem because the actual radius of a car on the track is less than 0.2 miles so the answer is less than 0.4π miles]

9. radius 6 feet, circumference 12π feet

10. diameter 14 cm, circumference 14π cm

11. diameter 4.8 feet, circumference 4.8π feet

2.83941151 would be the answer you're looking for! : )