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	140	140	170	210	200	330	280	390	440	450	400	590	610	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 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 60. (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.

Answer 1

(a) The linear regression equation is given as y_hat = -45.12 + 1.71 x, where y_hat is the predicted value of the NO_x emission rate (ppm) and x = given burner area liberation rate (MBtu/hr-ft²).

(b) the estimate of expected NO_x emission rate when the burner area liberation rate equals 215 is obtained by putting x = 215 in the above found linear regression equation in part (a). It comes out to be 322.53 ppm. (Rounded to two decimal places)

(c) The linear regression equation explains that when there is one unit change in the given burner area liberation rate (MBtu/hr-ft²)., there is 1.71 units increase in the value of NO_x emission rate (ppm). So, when the burner area liberation rate is decreased by 60, then the amount by which we expect the NO_x emission rate to change is 1.71*60 = 102.6 units.

(d) We plot the data and see that the data is perfectly linear with almost all the data points falling on the regression line, thus, we say that we would use the estimated regression line to predict emission rate for a liberation rate of 500. Option (1) --yes, the data is perfectly linear, thus lending to accurate predictions is the correct option.

The answers and graphs for verification are obtained using R-software. Code and output are attached below.