The table shows the amount of time spent practicing the piano by 8 music students versus the number of mistakes that they made in their recital.

Question

A table with heading 'Practice Time vs. Mistakes Made' is showing data of Practice Time in hours and Mistakes Made' as (4,6), (7,4), (3,7), (2,3), (10,2), (12,1), (9,2) and (6,8) respectively.

 

Suppose the table were extended to include 5 new data points. Choose the points such that when the data was graphed as a scatter plot it would show no correlation.
A. (4, 1), (6, 2), (8, 6), (10, 5), (12, 6)
B. (4, 5), (7, 3), (3, 7), (10, 1), (12, 1)
C. both of the above
D. none of the above

 

 

Please, i need help!

Answer 1

So you have the initial points of 4,6), (7,4), (3,7), (2,3), (10,2), (12,1), (9,2) and (6,8) respectively, you can graph it out to see it clearer.

(this format does not allow for graphs)

This is the initial relationship between the points provided to you in the question. You could visually sees that there is a weak correlation between the points because the points are all scattered. Then the R value (or Correlation coefficient) gives you a visual calculation of how close the data points are to being closely aligned, with "0" being really non correlated and "1" being highly correlated. The original is 0.4206, which is greater than zero but closer to zero than to 1 so we say it is a weak correlation.

So with this as a basis, lets graph both choice A and Choice B. One last note is that no correlation means that R value must 0 or very close to zero that we cannot say there is a correlation with the new data points

So Choice A (this format does not allow for graphs)

Very week with R^2 = 0.02. SO yes A is correct no correlation

Choice B (this format does not allow for graphs)

Choice B is out, In Choice B we have a greater correlation than the original at R^2 = 5914. So for the purpose of this question we do have correlation so any thing that includes B is automatically wrong.

So the answer is A, choices B and C are out because both include data set B and we saw B has a correlation. Choice D is out because A is correct so it is not none.