Question

Here is a bivariate data set.

x	y
44.1	57.5
28.1	30.4
19.3	21.1
19.4	7.6
23.9	22.7
23.6	25.6
36.5	43.3
47.5	56

Find the correlation coefficient and report it accurate to three decimal places.
r =

What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place.
r² = %

Answer 1

• Here Let X be the random variable denoting the independent variable and let Y be the random variable denoting the dependent variable .
• First we will calculate the sum of square of X and Y
• $ssx=\sum x^{2}-n\bar{x}^{2}$=8013.94-(8*30.05²)=789.92
• $ssy=\sum y^{2}-n\bar{y}^{2}$=10914.9-(8*33.0²)=2189.7
• $ssxy=\sum xy-n\bar{x}\bar{y}$=9219.8-(8*30.05*33.0)=1280.59

• Hence to calculate the correlation coefficient

• $r=\frac{SSxy}{\sqrt{SSxx*SSyy}}$=

• =0.973

• To calculate the coefficient of determination

• proportion of the variation in y can be explained by the variation in the values of x

• $R^{2}=\frac{SSxy^{2}}{SSxx*SSyy}$

• 0.948

• =94.8%
  

Answer 2

Here is a bivariate data set.

x	y
62	29.4
77.3	76
39.3	16.8
45.2	31.2
50.3	28.9
69.8	65.6
79.8	65
64.7	52.2

Find the correlation coefficient and report it accurate to three decimal places. 
r = 

What percentage of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place.
r² = %

Answer 3

ased on the data shown below, calculate the regression line (each value to at least two decimal places)

y =  x + 

x	y
4	25.22
5	24.75
6	25.98
7	27.31
8	28.44
9	29.97
10	29.5
11	32.03
12	34.66
13	35.39

Answer 4

ased on the data shown below, calculate the regression line (each value to two decimal places)

y =  x + 

x	y
3	25.01
4	26.28
5	27.05
6	30.82
7	32.39
8	32.96
9	38.43
10	36.9
11	38.87
12	41.64
13	45.21
14	47.98
15	48.65
16	52.82
17	54.19
18	54.16