Question

The accompnaying data were read from a graph that appeared in a recent study. The independent variable is SO₂ deposition rate (mg/m²/day) and the dependent variable is steel weight loss (g/m²).

x	14	18	40	43	45	112
y	280	350	470	500	560	1200

Calculate the residual for when SO₂ deposition rate is 40 mg/m²/day.

Answer 1

	X	Y	X * Y	X2	Ŷ	Residual = ( Y - Ŷ )
	14	280	3920	196	268.2375685	11.76243153
	18	350	6300	324	305.4838363	44.51616368
	40	470	18800	1600	510.3383095	-40.3383095
	43	500	21500	1849	538.2730104	-38.2730104
	45	560	25200	2025	556.8961443	3.103855655
	112	1200	134400	12544	1180.771131	19.22886908
Total	272	3360	210120	18538	3360	3.41061E-13

Equation of regression line is Ŷ = a + bX
b = ( n Σ(XY) - (ΣX* ΣY) ) / ( n Σ X² - (ΣX)² )
b = ( 6 * 210120 - 272 * 3360 ) / ( 6 * 18538 - ( 272 )²)
b = 9.3116

a =( ΣY - ( b * ΣX ) ) / n
a =( 3360 - ( 9.3116 * 272 ) ) / 6
a = 137.8756
Equation of regression line becomes Ŷ = 137.8756 + 9.3116 X

Residual for X = 40 is -40.3383095.