Question

13 The scatter plot for the data set X and Y shows the data points clustered in a nearly perfect circle. For these data, what is the most likely value for the Pearson r? a) near 0 b) r near +1 c) r near - 1 d) r between - 5 and 7.5 e) none of the above.

Answer 1

Here is the solution and explanation. Hope you find it useful.

The most likely value for the pearson r is near 0.

The trivial reason is since the data is circular in nature, there is no linear relationship between the two varieties.

assuming there are n observations.

r = coul,y) sd, .sdy cov(x,y) = {(1; – 7)(45 – )

Note that these values are such that the circle has centre near $\bar{x}$ and $\bar{y}$ . A easy interpretation would be :

In the graph of a circular cluster note that if you draw a line perpendicular to the x-axis at some value of x then it touches several y points in the cluster, i.e. for some x x val there are several y values. Then the sum in then for some specific $x_i$ there are say $n_i$ y observations. And say i = 1,2,..,n.

Then .

ι; κου(α, 9) - Σα - ) Συ; - 3) - Σ(ας – ) - 0} = 0

The sum can be written in this way since for each x observation there are multiple y observation. And those y observations when summed about their mean should give 0.

So the numerator of Pearson r becomes zero.