Question

1. Calculate and interpret r.

2. Calculate and interpret r²

	Weight	Fuel Efficiency
Car1	3162	19
Car2	2566	29
Car3	2785	25
Car4	3283	26
Car5	3496	20
Car6	1044	27
Car7	2100	14
Car8	2539	45
Car9	1082	36
Car10	3025	13
Car11	2187	43
Car12	2686	18
Car13	1059	20
Car14	961	22
Car15	1764	36
Car16	1394	38
Car17	2658	40
Car18	2110	37
Car19	1569	17
Car20	2701	24

Answer 1

Solution(a)
Coefficient correlation r can be calculated as
Coefficient correlation r = ((n*Xi*Yi)-(Xi*Yi))/sqrt(((n*Xi^2)-(Xi)^2))*((n*Yi^2)-(Yi)^2))
Here n = 20

Weight(X)	Fuel Efficiency(Y)	X^2	Y^2	XY
3162	19	9998244	361	60078
2566	29	6584356	841	74414
2785	25	7756225	625	69625
3283	26	10778089	676	85358
3496	20	12222016	400	69920
1044	27	1089936	729	28188
2100	14	4410000	196	29400
2539	45	6446521	2025	114255
1082	36	1170724	1296	38952
3025	13	9150625	169	39325
2187	43	4782969	1849	94041
2686	18	7214596	324	48348
1059	20	1121481	400	21180
961	22	923521	484	21142
1764	36	3111696	1296	63504
1394	38	1943236	1444	52972
2658	40	7064964	1600	106320
2110	37	4452100	1369	78070
1569	17	2461761	289	26673
2701	24	7295401	576	64824
44171	549	109978461	16949	1186589

Correlation coefficient r = ((20*1186589)-(44171*549))/sqrt(((20*109978461)-(44171*44171))*((20*16949)-(549*549))) = -518099/sqrt(248491979*37579) = -0.1695
Form the correlation coefficient r we can see that correlation coefficient is in negative that means both variables are negatively correlated with each other and both variables are very weakly correlated with each other.
Solution(b)
Coefficient of determination r^2 = (Coefficient correlation)^2 = (-0.1695)^2 = 0.0287
So r^2 or coefficient of determination tells us that this model explains 2.87% variation in dependent variable due to variation in independent variable.