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 140 140 180 220 200 320 270 410 440 440 390 580 600 670 (a) Assuming that the simple linear regression model is valid, obtain the least squares estimate of the true regression line. (Give answers accurate to 2 decimal places.) y = ____ + _____x (b) What is the estimate of expected NOx emission rate when burner area liberation rate equals 250? (Give answer accurate to 1 decimal place.) _____ ppm (c) Estimate the amount by which you expect NOx emission rate to change when burner area liberation rate is decreased by 60. (Give answer accurate to 1 decimal place.) _____ ppm 

          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
180
220
200
320
270
410
440
440
390
580
600
670

(a) Assuming that the simple linear regression model is valid, obtain the least squares estimate of the true regression line. (Give answers accurate to 2 decimal places.)
y = ____ + _____x

(b) What is the estimate of expected NOx emission rate when burner area liberation rate equals 250? (Give answer accurate to 1 decimal place.)
_____ ppm

(c) Estimate the amount by which you expect NOx emission rate to change when burner area liberation rate is decreased by 60. (Give answer accurate to 1 decimal place.)
_____ ppm
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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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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 140 140 180 220 200 320 270 410 440 440 390 580 600 670 (a) Assuming that the simple linear regression model is valid, obtain the least squares estimate of the true regression line. (Give answers accurate to 2 decimal places.) y = ____ + _____x (b) What is the estimate of expected NOx emission rate when burner area liberation rate equals 250? (Give answer accurate to 1 decimal place.) _____ ppm (c) Estimate the amount by which you expect NOx emission rate to change when burner area liberation rate is decreased by 60. (Give answer accurate to 1 decimal place.) _____ ppm
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Transcript

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00:01 Hello students, let us do this question.
00:04 In this question we have to estimate the regression equation for the given values of x and y.
00:10 Here x is our independent variable and y is dependent variable.
00:14 X is given as burner area liberation rate and y is given as nox emission rate.
00:34 We can use excel function to get the regression equation.
00:38 For this we have to enter the values of x and y into the two separate columns.
00:42 In excel.
00:45 Now the regression equation is given as y hat equal to intercept plus slope into x or we can rewrite it as beta not plus beta 1 x where beta not is the y intercept and beta is the slope.
01:09 The excel functions which we can use here to get the regression equation to get the slope of the line the excel function is in any empty cell, first enter equal to sign, then write the function slope, then open parenthesis, first enter the values of or select the data where the y values are entered and then select the data where the x values are entered.
01:37 After this, we will get the slope of the regression line as 1 .68.
01:47 Now, in the same way, we can get the intercept, beta, not, with the.
01:53 The excel as the function is intercept, inter first the y values and then the x values.
02:03 This will give us the intercept value as minus 39 .95.
02:12 So using these values, the regression equation is, 5 hat equal to minus 39 .95 plus 1 .68 to x.
02:27 This is the regression equation for the given data...
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