Question

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 4 5 6

y 49 43 33 26

Complete parts (a) through (e), given Σx = 15, Σy = 151, Σx² = 77, Σy² = 6015, Σxy = 493, and r ≈ −0.906.

(a) Draw a scatter diagram displaying the data.

(b) Verify the given sums Σx, Σy, Σx², Σy², Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

Σx =

Σy =

Σx² =

Σy² =

Σxy =

r =

(c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

x =

y =

^y = + x

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(e) Find the value of the coefficient of determination r². 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? (Round your answer for r² to three decimal places. Round your answers for the percentages to one decimal place.)

r² =

explained     %

unexplained     %

(f) If a team had x = 3 fouls over and above the opposing team, what does the least-squares equation forecast for y? (Round your answer to two decimal places.)

%

Answer 1

Solution:

Here given information is given Σx = 15, Σy = 151, Σx² = 77, Σy² = 6015, Σxy = 493, and r ≈ −0.906.

Using minitab statistical software we solve all the problem as below

a)scatter diagram

Comment : using scatter plot we say that there is negative correlation between x and y because if value value of x increase then value of y decreases .

b)

Here  Σx = 15, Σy = 151, Σx² = 77, Σy² = 6015, Σxy = 493, and r ≈ −0.906.

Question a) is correct.

c)

Regression line Equation of given data is

Y = 50.99 - 3.53 X

(d) Graph the least-squares line.

comment : Here all the data points are lies on the line or near to regression line it means that data is approximately normal distributed.

e)

coefficient of determination r²

^{R-sq = 82.15%}
82.15 percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line.

(f) If a team had x = 3 fouls over and above the opposing team, what does the least-squares equation forecast for y?

therefore put x= 3

Y = 50.99 - 3.53 X

Y = 50.99 - (3.53 * 3)

Y = 40.4

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