The following data is representative of that reported in an

The following data is representative of that reported in an article on nitrogen emissions with x-burner area beration rate M tu hr a indy-NO emis on te m x 100 125 125 150 150 200 200 250 250 300 300 350 400 400 y 160 130 190 210 180 320 270 400 430 440 380 610 620 670 (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 245? (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 40. (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

Solution

Let the linear regression equation is :

Y = A + B.X

Where,

X ( independent variable ) = Burner area liberation rate

Y ( Dependent variable ) = NO2 emission rate

A, B = Constants

We place all values of X and Y as given in the problem into 2 parallel columns in excel and apply the formula LINEST ( ) and obtain following :

A = - 49.02

B = 1.726

Thus , regression Line is : Y = 1.726.X – 49.02

Y = 1.726X – 49.02

When burner area liberation rate i.e. X = 245,

Y = 1.726 X 245 – 49.02 = 422,87 – 49.02 = 373.85

ESTIMATE OF EXPECTED NO2 EMISSION RATE = 373.85 PPM

When burner area liberation rate decreases by 40, change in NO2 emission rate

= B x 40 = 1.726 x 40 = 69.04

NO2 EMISSION RATE WILL CHANGE BY 69.04

We can use the linear regression equation to predict estimated emission rate for liberation rate of 500 , by putting X = 500 and derive value of Y accordingly. The data is linear and will lead to perfect prediction.

YES, THE DATA IS PEFECTLY LINEAR LEADING TO ACCURATE PREDICTION

Y = 1.726X – 49.02