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 150 150 190 210 180 330 290 390 430 440 390 600 610 670 (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.) (b what is the estimate of expected NOx emission rate when burner area liberation rate equals 215 Round your ans erto o decima 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? O Yes, the data is perfectly linear, thus lending to accurate predictions. O Yes, this value is between two existing values. No, this value is too far away from the known valuesor seful extrapolation No, the data near this point deviates from the overall regression model.

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = -40.282523 + 1.695138 x
Sample size: 14
R (correlation coefficient) = 0.97939217
R-sq = 0.95920902
Estimate of error standard deviation: 37.199592

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

a) Regression equation is:

y = -40.2825 + 1.6951 x

b) For x = 215,

y = 324.17 ppm

c) Estimated change = 1.6951(50) = 84.76 ppm

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -40.282523 25.780394 0 12 -1.5625255 0.1441 Slope 1.695138 0.10091132 0 12 16.798294 <0.0001

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