In: Statistics and Probability
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 | 140 | 140 | 190 | 200 | 190 | 310 | 290 | 410 | 420 | 450 | 400 | 600 | 600 | 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 NOx
emission rate when burner area liberation rate equals 240? (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
(d) Would you use the estimated regression line to predict emission
rate for a liberation rate of 500? Why or why not?
Yes, the data is perfectly linear, thus lending to accurate predictions. Yes, this value is between two existing values. No, this value is too far away from the known values for useful extrapolation. No, the data near this point deviates from the overall regression model.
a)
y^ =-48.8528+1.7170*x
b)
predicted val=-46.8528+240*1.717= | 365.23 |
(please try 365.22 if this comes wrong)
c)
change = 1.7170*(-50)= -85.85
d)
No, this value is too far away from the known values for useful extrapolation