The following data is representative of that reported in an article on nitrogen

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 = NOx emission rate (ppm)

: x 100 125 125 150 150 200 200 250 250 300 300 350 400 400

y 160 140 180 200 180 330 290 400 440 450 400 610 620 660

(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 NOx emission rate when burner area liberation rate equals 250? (Round your answer to two decimal places.) ppm

(c) Estimate the amount by which you expect NOx emission rate to change when burner area liberation rate is decreased by 50. (Round your answer to two decimal places.) ppm

Explanation / Answer

A)

XY and X2 as it was done in the table below.

the sum of every column:

X=3300 , Y=5060 , XY=1427500 , X2=913750

USING THE FORMULA FOR A AND B

WE WILL GET a = -45.82

b = 1.72

hence regression = y = -45.82 +1.72x

b) we have to find y when x = 250

therefore y = -45.82 + 1.72*250

= 384.18

c) when the burnet area is decreased by 50% then the nox exmission will also decrease by 50% as both are directly proportional

X Y XY XX 100 160 16000 10000 125 140 17500 15625 125 180 22500 15625 150 200 30000 22500 150 180 27000 22500 200 330 66000 40000 200 290 58000 40000 250 400 100000 62500 250 440 110000 62500 300 450 135000 90000 300 400 120000 90000 350 610 213500 122500 400 620 248000 160000 400 660 264000 160000

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