x
|
6.1 |
5.6 |
4.0 |
5.2 |
6.2 |
6.5 |
11.1 |
y
|
−1.8
|
−4.0
|
−7.2
|
−4.0
|
3.6 |
−0.1
|
−4.4
|
Complete parts (a) through (e), given Σx = 44.7,
Σy = −17.9,
Σx
2 = 315.51, Σy
2 = 119.41,
Σxy = −110.15,
andr ≈ 0.0883.
(a) Draw a scatter diagram displaying the data.
(b) Verify the given sums Σx, Σy, Σx
2, Σy
2, Σxy, and the value of the sample correlation coefficientr. (Round your value forr to four 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 answer to four decimal places.)
(e) Find the value of the coefficient of determinationr
2. What percentage of the variation iny can beexplained by the corresponding variation inx and the least-squares line? What percentage isunexplained? (Round your answer forr
2 to four decimal places. Round your answers for the percentages to two decimal place.)
r
2 = |
|
explained |
% |
unexplained |
% |
(f) Considering the values ofr andr
2, does it make sense to use the least-squares line for prediction? Explain your answer.
The correlation between the variables is so high that it does not make sense to use the least-squares line for prediction.
The correlation between the variables is so low that it does not make sense to use the least-squares line for prediction.
The correlation between the variables is so high that it makes sense to use the least-squares line for prediction.
The correlation between the variables is so low that it makes sense to use the least-squares line for prediction.