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):x100125125150150200200250250300300350400400y160140190210200320280400440430400600600660(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 240? (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. An article gave a scatter plot along with the least squares line of x = rainfall volume (m3) and y = runoff volume (m³) for a particular location. The accompanying values were read from the plot.x 8 12 14 16 23 3040 51 55 6767 72 81 96 112 12772y 4 10 13 15 15 25 27 45 38 46 53 67 82 99 102(a) Does a scatter plot of the data support the use of the simple linear regression model?O Yes, the scatterplot shows a reasonable linear relationship.O Yes, the scatterplot shows a random scattering with no pattern.O No, the scatterplot shows a reasonable linear relationship.O No, the scatterplot shows a random scattering with no pattern.(b) Calculate point estimates of the slope and intercept of the population regression line. (Round your answers to four decimal places.)slopeintercept(c) Calculate a point estimate of the true average runoff volume when rainfall volume is 55. (Round your answer to four decimal places.)m³(d) Calculate a point estimate of the standard deviation 6. (Round your answer to two decimal places.)m³3(e) What proportion of the observed variation in runoff volume can be attributed to the simple linear regression relationship between runoff and rainfall? (Round your answer to four decimal places.)

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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

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ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

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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 = NO_x emission rate (ppm):

x	100	125	125	150	150	200	200	250	250	300	300	350	400	400
y	160	140	190	210	200	320	280	400	440	430	400	600	600	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 240? (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.