Question

Fill in all the underlined spots on the spreadsheet with the data about Absorbance of Light for different Nitrate Levels. The goals are: 1) to compute the correlation and slope of the regression line by using the "SS formulas" and 2) to compute SSE, the sum of the squared "errors" (residuals).

Data from Exercise 2.69 (p. 97)
The absorbance of Light for Different Nitrate Levels
							y - that
	Nitrates x (mg/liter of water)	Absorbance y	x^2 values	y^2 values	x*y values	y hat (predicted absorbances)	residuals/errors	squared residuals
	50	7	_____	_____	_____	_____	_____	_____
	50	7.5	_____	_____	_____	_____	_____	_____
	100	12.8	_____	_____	_____	_____	_____	_____
	200	24	_____	_____	_____	_____	_____	_____
	400	47	_____	_____	_____	_____	_____	_____
	800	93	_____	_____	_____	_____	_____	_____
	1200	138	_____	_____	_____	_____	_____	_____
	1600	183	_____	_____	_____	_____	_____	_____
	2000	230	_____	_____	_____	_____	_____	_____
	2000	226	_____	_____	_____	_____	_____	_____
Sums	8400	968.3	_____	_____	_____		SSE	_____
Means	840	96.83
Std Devs	802.7037644	90.95273559
Correlation	0.999939232
Coefficient of Determination	0.999878467		SSxx	_____
			SSyy	_____
Slope	0.113301086		SSxy	_____
Intercept	1.657087429
			Correlation	_____
Regression Equation	y = 0.1133x + 1.6571		Slope	_____

Answer 1

Completed Table

	Nitrates x (mg/liter of water)	Absorbance y	x^2 values	y^2 values	x*y values	y hat (predicted absorbances)	residuals/errors	squared residuals
	50	7	2,500	49	350	7.32	-0.32	0.10
	50	8	2,500	56	375	7.32	0.18	0.03
	100	13	10,000	164	1,280	12.99	-0.19	0.04
	200	24	40,000	576	4,800	24.32	-0.32	0.10
	400	47	1,60,000	2,209	18,800	46.98	0.02	0.00
	800	93	6,40,000	8,649	74,400	92.30	0.70	0.49
	1,200	138	14,40,000	19,044	1,65,600	137.62	0.38	0.15
	1,600	183	25,60,000	33,489	2,92,800	182.94	0.06	0.00
	2,000	230	40,00,000	52,900	4,60,000	228.26	1.74	3.03
	2,000	226	40,00,000	51,076	4,52,000	228.26	-2.26	5.10
Total	8,400	968	128,55,000	1,68,212	14,70,405			9.05

SSE = ∑Squared residuals = 9.05

SS_X = ∑X² – (∑X)²/n = 128,55,000 – (8400)²/10 = 57,99,000

SS_Y = ∑Y² – (∑Y)²/n = 168212 – (968)²/10 = 74,452

SS_XY = ∑XY – (∑X*∑Y)/n = 1470405 – (8400*968)/10 = 6,57,033

SS_Reg = (SS_XY)²/SS_X = 74442.55

SS_Total = SS_Y

Correlation Coefficient = (SS_Reg / SS_Total)^1/2 = 0.999939

Slope = SS_XY/SS_X = 6,57,033/57,99,000 = 0.113301