Question

Several scientists decided to travel to South America each year beginning in 2001 and record the number of insect species they encountered on each trip. The table shows the values coding 2001 as 1,2002 as 2, and so on. Find the model that best fits the data and identify its corresponding R² value.   Year: 1,2,3,4,5,6,7,8,9,10 Species: 47,53,38,35,49,42,60,54,67,82

Answer 1

	Year ( X )	Species ( Y )	X * Y	X2
	1	47	47	1
	2	53	106	4
	3	38	114	9
	4	35	140	16
	5	49	245	25
	6	42	252	36
	7	60	420	49
	8	54	432	64
	9	67	603	81
	10	82	820	100
Total	55	527	3179	385

Regression Equation is  

b = 3.4

a = 34

Regression equation becomes

Coefficient of Determination R²

	Year ( X )	Species ( Y )	X * Y	X2	Y2
	1	47	47	1	2209
	2	53	106	4	2809
	3	38	114	9	1444
	4	35	140	16	1225
	5	49	245	25	2401
	6	42	252	36	1764
	7	60	420	49	3600
	8	54	432	64	2916
	9	67	603	81	4489
	10	82	820	100	6724
Total	55	527	3179	385	29581

Coefficient of correlation

R² = r² = ( 0.7263 )² = 0.5275