You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the Bar-S herd. How much should a healthy calf weigh? Letx be the age of the calf (in weeks), and lety be the weight of the calf (in kilograms).
x
|
3 |
3 |
12 |
16 |
26 |
36 |
y
|
42 |
50 |
71 |
100 |
150 |
200 |
Complete parts (a) through (e), given Σx = 96, Σy = 613, Σx
2 = 2390, Σy
2 = 81,805, Σxy = 13,828, andr ≈ 0.993.
(a) Draw a scatter diagram displaying the data.
Flash Player version 10 or higher is required for this question.
You can get Flash Player free from Adobe's website.
(b) Verify the given sums Σ
x, Σ
y, Σ
x2, Σ
y2, Σ
xy, and the value of the sample correlation coefficient
r. (Round your value for
r to three decimal places.)
Σx = |
|
Σy = |
|
Σx
2 = |
|
Σy
2 = |
|
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.)
(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.)
r
2 = |
|
explained |
% |
unexplained |
% |
(f) The calves you want to buy are 21 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.)
kg
2.Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let
x be the weight of the car (in hundreds of pounds), and let
y be the miles per gallon (mpg).
x
|
27 |
43 |
32 |
47 |
23 |
40 |
34 |
52 |
y
|
29 |
22 |
22 |
13 |
29 |
17 |
21 |
14 |
Complete parts (a) through (e), given Σ
x = 298, Σ
y = 167, Σ
x2 = 11,800, Σ
y2 = 3745, Σ
xy = 5833, and
r ≈ −0.911.
(a) Draw a scatter diagram displaying the data.
Flash Player version 10 or higher is required for this question.
You can get Flash Player free from Adobe's website.
(b) Verify the given sums Σ
x, Σ
y, Σ
x2, Σ
y2, Σ
xy, and the value of the sample correlation coefficient
r. (Round your value for
r to three decimal places.)
Σx = |
|
Σy = |
|
Σx
2 = |
|
Σy
2 = |
|
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.)
(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.)
r
2 = |
|
explained |
% |
unexplained |
% |
(f) Suppose a car weighs
x = 36 (hundred pounds). What does the least-squares line forecast for
y = miles per gallon? (Round your answer to two decimal places.)
mpg
3.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.
Complete parts (a) through (e), given Σ
x = 16, Σ
y = 154, Σ
x2 = 78, Σ
y2 = 6302, Σ
xy = 548, and
r ≈ −0.941.
(a) 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.)
r
2 = |
|
explained |
% |
unexplained |
% |
(b) 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.)
%