Question

In: Math

The following data is representative of that reported in an article on nitrogen emissions, with x...

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 140 140 170 210 200 330 280 390 440 450 400 590 610 660

(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 NOx 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 NOx 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.

Solutions

Expert Solution

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

(b) the estimate of expected NOx 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 NOx emission rate (ppm). So, when the burner area liberation rate is decreased by 60, then the amount by which we expect the NOx 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.


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