Question

If an object is dropped from a height, its downward speed theoretically increases
linearly over time because the object is subject to the steady pull of gravity. Here
are observational data on the speed of a ball dropped from a certain height at time
x = 0:
Time (seconds) X 0 0.2 0.4 0.6 0.8
Speed (m/sec) Y 0 1.92 3.58 6.01 7.88

Answer 1

@xMissAlyCatx

Answer 2

what was the correlation in the other one we did? .99 something??

Answer 3

0.99847175

Answer 4

I think it is \(r=0.99847175\) not \(r^2\) am I right?

Answer 5

what I know, is if the coefficient of correlation \(r\) is close to 1, or it is close to -1, then we have a strong correlation or a strong causality relation, between the two involved variables

Answer 6

then qhT IS R2

Answer 7

*what is r2 then

Answer 8

sincerely I don't know, maybe it can be the square of the coefficient of correlation \(r\)

Answer 9

in such case (\(r^2=0.99847175\)) we can state that there is a strong causality relation between the involved variables

Answer 10

since we can write this:
\[\huge r \approx 1 \Rightarrow {r^2} \approx 1\]

Answer 11

so what would you suggest I put as a correct answer?

Answer 12

or:
\[\huge r \approx - 1 \Rightarrow {r^2} \approx 1\]
yes! I think so!

Answer 13

i should put that?

Answer 14

yes! I suggest to write that \(r^2\) is the square of the coefficient correlation, and it represents a measure of how are strongly correlated the experimental data

Answer 15

ok and r2 equals 1 right?

Answer 16

from your computation I see that \(r^2=0.99847175\) am I right?

Answer 17

yes you are

Answer 18

ok! :) so we can write \(r^2=0.998\) and such value verifies the condition:
\[\huge {r^2} \approx 1\]
namely the condition of strong causal correlation between the involved variables