Questions: Refer to the accompanying scatterplot. a. Examine the pattern of all 10 points and subjectively determine whether there appears to be a strong correlation between x and y. b. Find the value of the correlation coefficient r and determine whether there is a linear correlation. c. Remove the point with coordinates (10,9) and find the correlation coefficient r and determine whether there is a linear correlation. d. What do you conclude about the possible effect from a single pair of values?

Solution Steps

Visually, there appears to be some positive correlation due to the outlier point (10,9). Without this point, the remaining data points appear to have no correlation as they cluster around the same x-values with different y-values.

No, the overall data does not suggest a strong linear correlation.

To calculate the correlation coefficient _r_, we need the coordinates of all data points. From the scatterplot, the data points are (1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3), and (10,9).

We use the formula:

$r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n(\sum x^2) - (\sum x)^2][n(\sum y^2) - (\sum y)^2]}}$

Where $n=10$.

$\sum x = 1+1+1+2+2+2+3+3+3+10 = 28$ $\sum y = 1+2+3+1+2+3+1+2+3+9 = 27$ $\sum x^2 = 1+1+1+4+4+4+9+9+9+100 = 142$ $\sum y^2 = 1+4+9+1+4+9+1+4+9+81 = 122$ $\sum xy = 1+2+3+2+4+6+3+6+9+90 = 126$

$r = \frac{10(126) - (28)(27)}{\sqrt{[10(142) - (28)^2][10(122) - (27)^2]}} = \frac{1260 - 756}{\sqrt{(1420 - 784)(1220 - 729)}} = \frac{504}{\sqrt{(636)(491)}} = \frac{504}{\sqrt{313116}} \approx \frac{504}{559.57} \approx 0.901$

Final Answer: