Question

Use a calculator to find the correlation coefficient of the data set. PLEASE HELP!

Answer 1

Answer:

The correlation coefficient of the data set is -0.901

Step-by-step explanation:

x           y            xx          xy          yy

1         20            1            20         400

3        14             9           42          196

5        10            25          50          100

9         6            81           54           36

15       4            225         60           16

$\sum x = 1+3+5+9+15=33\\\sum y =20+14+10+6+4=54\\\sum x^2 =1+9+25+81+225=341\\\sum y^2=400+196+100+36+16=748\\\sum xy=20+42+50+54+60=226$

Formula :$\frac{N \sum XY - (\sum X)(\sum Y)}{\sqrt{N\sum X^2 - (\sum X)^2}\sqrt{N \sumY^2 - (\sum Y)^2)}}$

$= \frac{5 (226) - (33)(54)}{\sqrt{5(341)- (33)^2}\sqrt{5 (748) - (54)^2}}\\=-0.901$

So, Option D is true

Hence the correlation coefficient of the data set is -0.901