Question

x= 3.1, 9.4, 1.2, 1.0, 9.0, 5.0, 3.4, 7.4, 0.1, 7.5

y= 8.9, 15.0, 4.8, 6.0, 14.9, 11.9, 9.8, 15.0, 4.7, 13.0


what is the coefficient of determination for this data set?

Answer 1

Table for Calculating Coefficient of Determination

We have, coefficient of determination = r² ,where r is the correlation coefficient between x and y.

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

Here, $n=10,\sum x =47.1, \sum y=104, \sum x^2=328.99, \sum y^2=1239, \sum xy=616.24$

Applying the formula,

$r=\frac{10\times 616.24-47.1\times104}{\sqrt(10\times328.99-(47.1)^2)(10\times1239-(104)^2)}$ = 0.9733 (rounded to 4 decimal places)

$\therefore$ Coefficient of determination = r² = (0.9733)² = 0.9473 (rounded to 4 decimal places)

Answer: The coefficient of determination of the given data is 0.9473.