Simplify

write your answer using only positive exponents. evaluate any numerical powers.

a) -0.717

b) -0.835

Step-by-step explanation:

The correlation coefficient r can be computed as

a)

xy          x²      y²      xy

0.028.00.00784.000.00

0.068.80.004733.440.00

0.226.80.04718.245.36

0.538.3  0.251466.8919.15

0.548.20.252323.2424.10

1.030.91.00        954.8130.90

1.226.7         1.44  712.8932.04

1.98.0    3.6164.0015.20

2.64.4    6.76        19.3611.44

3.37.2    10.8951.8423.76

4.76.8       22.09  46.2431.96

6.56.6       42.25  43.5642.90

sumx= 22.4

sumy= 300.7

sumx²= 88.58

sumy²= 11918.5

sumxy= 236.81

r= -0.717

So, the required correlation coefficient is -0.717.

b)

Firstly we take the square root of x and y values and then following calculations are made.

x             y           x²      y²     x*y

0.000005.291500.028.00.00000

0.000008.294580.068.80.00000

0.447215.176870.226.82.31517

0.707116.188700.538.3        4.37607

0.707116.942620.548.24.90918

1.000005.558781.030.95.55878

1.095455.167201.226.7  5.66039

1.378402.828431.98.0  3.89872

1.612452.097622.64.4    3.38231

1.816592.683283.37.2    4.87442

2.167952.607684.76.8    5.65332

2.549512.569056.56.6    6.54981

sumx= 13.4818

sumy= 55.4063

sumx²=  22.4

sumy²= 300.7

sumxy= 47.1782

So, the required correlation coefficient is -0.8353.