Question

Find the 2^nd order parabola (Ŷ = a₀ + a₁ x + a₂ x²) that fits to the following data set. Then calculate correlation coefficient.

x	0	1	2	3	4	5
y	2.1	7.7	13.6	27.2	40.9	61.1

Answer 1

The given data is inputted in EXCEL here and the SCATTERPLOT is used to obtain the scatterplot here. The TRENDLINE function is used to obtain the scatteplot after that and a 2nd degree polynomial is fitted on the above data.

y v = 1.8607 + 2.3593x + 2.4786 R = 0.9985 70 60 150 140 130 20 10 10 0 1 2 3 4 5 6

therefore the equation here is given as:

y = 2.4786 +2.3593.c + 1.8607.02

The coefficient of determination is obtained here to be: R2 = 0.9985

Therefore correlation coefficient now is computed here as:

$r = \sqrt{R^2} = \sqrt{0.9985} = 0.9992$

Therefore 0.9992 is the correlation coefficient here.