SOLUTION: The following sample observations were randomly selected: x: 11 2 11 5 9 11 20 1 y: 8 1 2 3 7 16 4 20

Question 1206835: The following sample observations were randomly selected:

x:
11
2
11
5
9
11
20
1
y:
8
1
2
3
7
16
4
20

a. Determine the coefficient of correlation. (Negative answer should be indicated by a minus sign. Round the final answer to 2 decimal places.)

Coefficient of correlation

b. Determine the coefficient of determination. (Round the intermediate calculations to 2 decimal places and final answer to 4 decimal places.)

Coefficient of determination

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i used the regression calculator at https://www.statskingdom.com/linear-regression-calculator.html to solve this.

there are lots of them on the web.
just pick the one that you understand the most, after doing some research.

hear are the results from using his calculator.

information you want to pay attention to is:

formula is y = -.2591 * x + 9.892.

-.2591 is the slope of the regression line.
9.892 is the y-intercapt (value of y when value of x is 0).

r = -.2293 which is a very small correlation in a downward direction, meaning as value of x goes up, value of y goes down.

r^2 = .05257. meaning only about 5% of the y-values are directly as a consequence of the x-values, meaning that the correlation is very weak.

p-value of .5849 is much higher than a critical p-value of .05 meaning that there is not sufficient evidence that the correlation is different than the assumed status quo.
this means that, if there was an assumed correlation different from this, this data would not be strong enough to say it should be this correlation instead.

here's a reference that includes how to interpret p-value in a regression analysis.

https://statisticsbyjim.com/regression/interpret-coefficients-p-values-regression/
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