It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game.

X= 0 2 5 6
Y= 50 45 33 26

Complete parts (a) through (e), given Σx = 16, Σy = 154, Σx2 = 78, Σy2 = 6302, Σxy = 548, and r ≈ −0.941.

a. Draw a scatter diagram displaying the data.
b. Find X- bar, Y- bar, a and b. Then find the equation of the least squares line y=a+bx.
c. Graph the least squares line on your scatter diagram. Be sure to use the point ( X-bar, Y- bar) as one of the points on the line.
d. Find the value of the coefficient of determination r ^2. What percentage of the variation in y can be explained by the corresponding variation in x and the least squares line? What percentage is unexplained?
e. If a team had x = 4 fouls over and above the opposing tem, what does the leas squares equation forecast for y?

a) First figure attached

b)

c)

And the slope would be:

And we can find the intercept using this:

So the line would be given by:

d)

So then the porcentage of variation explained is 88.5%

And the percentage of unexplained variation would be 100-88.5=11.5%

e) Using the least squares regression:

Using the excel equation with the we have:

Step-by-step explanation:

We assume that the data is this one:

x: 0,2,5,6

y: 50,45,33,26

Part a

For this case on the figure attached we see the scatter plot of the data.

Part b

Find the least-squares line appropriate for this data.  

For this case we need to calculate the slope with the following formula:

Where:

So we can find the sums like this:

With these we can find the sums:

And the slope would be:

And we can find the intercept using this:

So the line would be given by:

Part c

For this case we add the point (4.38.5) for the data and we got the equation as we can see on the figure attached.

y = -3.8578x + 51.616 (Equation adjusted with Excel)

Part d

So then the porcentage of variation explained is 88.5%

And the percentage of unexplained variation would be 100-88.5=11.5%

Part e

Using the least squares regression:

Using the excel equation with the we have:

(A) The prism could be a cube with a side length of 10 mm.

(B) It is possible for the length to be 1,000 mm.

(D) It is possible that the length is 2.5 mm.

Explanation:

Volume = l×w×h

where l is the length, w is the width and h is the height

It is possible that the length is 2.5 mm

Then volume = 2.5 × 10 ×40 = 1000 mm³

It is possible for length to be 1000 mm

Then volume = 1000 × 0.1 × 10 = 1000 mm³

The prism could be a cube of length 10 mm

Then volume = 10 × 10 × 10 = 1000 mm³