Question

What is the coefficient of determination for Data Set​ B? Full Data​ Set: Data Set A Data Set B Data Set C x y x y x y 3.6 8.9 3.1 8.9 2.8 8.9 8.3 15.0 9.4 15.0 8.1 15.0 0.5 4.8 1.2 4.8 3.0 4.8 1.4 6.0 1.0 6.0 8.3 6.0 8.2 14.9 9.0 14.9 8.2 14.9 5.9 11.9 5.0 11.9 1.4 11.9 4.3 9.8 3.4 9.8 1.0 9.8 8.3 15.0 7.4 15.0 7.9 15.0 0.3 4.7 0.1 4.7 5.9 4.7 6.8 13.0 7.5 13.0 5.0 13.0 ​(This is a reading assessment question. Be certain of your answer because you only get one attempt on this​ question.) The coefficient of determination for Data Set B is nothing​%. ​(Type an integer or decimal rounded to the

Answer 1

Answer: the coefficient determination of dataset B is 1.00

Step-by-step explanation:

Given Dataset B

x          y          xy            x²           y²

3.1      8.9      27.59      9.61        79.21

9.4     15.0     141           88.36     225

1.2      4.8       5.76        1.44        23.04

1          6          6              1            36

9        14.9     134.1          81         222.01

5        11.9      59.5         25         141.61

3.4      9.8      33.32      11.69       96.04

7.4      15.0     111           54.76      225

0.1       4.7      0.47        0.01        22.09

7.5       13       97.5        56.25      169

∑x=47.1, ∑y=104, ∑xy=616.24, ∑x²=329.12, ∑y²=1239

Now to find the coefficient determination ( r² )

we need to first find r

r = { n(∑xy) - (∑x)(∑y) } / { √( [n∑x² - (∑x)²] [n∑y² - (∑y)²] )

so we substitute

r = { 10(616.24) - (47.1)(104)} / { √( [10(329.12) - (47.1)²] [10(1239) - (104)²] )

r = 1264 / 1299.45

r = 0.97

now the coefficient determination is ( r² )

so coefficient determination = r²

= (0.97)²

= 0.9409 ≈ 1.00 (integer)

Therefore the coefficient determination of dataset B is 1.00