Question

The following data is representative of that reported in an article on nitrogen emissions, with x = burner area liberation rate (MBtu/hr-ft²) and y = NO_x emission rate (ppm):

x	100	125	125	150	150	200	200	250	250	300	300	350	400	400
y	160	140	190	210	180	320	270	410	430	450	390	610	610	670

(a) Assuming that the simple linear regression model is valid, obtain the least squares estimate of the true regression line. (Round all numerical values to four decimal places.)
y =

(b) What is the estimate of expected NO_x emission rate when burner area liberation rate equals 215? (Round your answer to two decimal places.)
ppm

(c) Estimate the amount by which you expect NO_x emission rate to change when burner area liberation rate is decreased by 40. (Round your answer to two decimal places.)
ppm

Answer 1

Folloiwng table shows the caculations:

	X	Y	X^2	Y^2	XY
	100	160	10000	25600	16000
	125	140	15625	19600	17500
	125	190	15625	36100	23750
	150	210	22500	44100	31500
	150	180	22500	32400	27000
	200	320	40000	102400	64000
	200	270	40000	72900	54000
	250	410	62500	168100	102500
	250	430	62500	184900	107500
	300	450	90000	202500	135000
	300	390	90000	152100	117000
	350	610	122500	372100	213500
	400	610	160000	372100	244000
	400	670	160000	448900	268000
Total	3300	5040	913750	2233800	1421250

(b)

Answer: 324.44 ppm

(c)

For each unit decrease in burner area liberation rate, NOx is decreased by 1.7164 units. So the amount by which you expect NOx emission rate to change (that is decreased by) when burner area liberation rate is decreased by 40 is

40 * 1.7164 = 68.656

Answer: 68.66 ppm