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a. Assuming that a simple linear regression model is appro- priate, fit the regression model relating BOD (y) to the time (x). What is the estimate of o²? b. What is the estimate of expected BOD level when the time is 15 days? c. What change in mean BOD is expected when the time changes by 3 days? d. Suppose that the time used is 6 days. Calculate the fitted value of y and the corresponding residual. e. Calculate the fitted ŷ, for each value of x; used to fit the model. Then construct a graph of ŷ, versus the corresponding observed values y; and comment on what this plot would look like if the relationship between y and x was a deterministic (no random error) straight line. Does the plot actually obtained indicate that time is an effective regressor variable in pre- dicting BOD? 11.2.9 WP An article in the Journal of the Environmental Engineering Division ["Least Squares Estimates of BOD Param- eters" (1980, Vol. 106, pp. 1197-1202)] took a sample from the Holston River below Kingport, Tennessee, during August 1977. The biochemical oxygen demand (BOD) test is conducted over a period of time in days. The resulting data follow: Time (days): 1 2 4 68 10 12 14 16 18 20 BOD (mg/liter): 0.6 0.7 1.5 1.9 2.1 2.6 2.9 3.7 3.5 3.7 3.8

a. Assuming that a simple linear regression model is appro- priate, fit the regression model relating BOD (y) to the time (x). What is the estimate of o²? b. What is the estimate of expected BOD level when the time is 15 days? c. What change in mean BOD is expected when the time changes by 3 days? d. Suppose that the time used is 6 days. Calculate the fitted value of y and the corresponding residual. e. Calculate the fitted ŷ, for each value of x; used to fit the model. Then construct a graph of ŷ, versus the corresponding observed values y; and comment on what this plot would look like if the relationship between y and x was a deterministic (no random error) straight line. Does the plot actually obtained indicate that time is an effective regressor variable in pre- dicting BOD? 11.2.9 WP An article in the Journal of the Environmental Engineering Division ["Least Squares Estimates of BOD Param- eters" (1980, Vol. 106, pp. 1197-1202)] took a sample from the Holston River below Kingport, Tennessee, during August 1977. The biochemical oxygen demand (BOD) test is conducted over a period of time in days. The resulting data follow: Time (days): 1 2 4 68 10 12 14 16 18 20 BOD (mg/liter): 0.6 0.7 1.5 1.9 2.1 2.6 2.9 3.7 3.5 3.7 3.8

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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Please answer Q11.4.9 & Q11.2.9 stepwise please 

11.4.9 Consider the data in Exercise 11.2.9 on y=oxygen demand and x = time.
a. Test for significance of regression using α = 0.01. Find the P-value for this test.  What conclusions can you draw?
b. Estimate the standard errors of the slope and intercept
c. Test the hypothesis that β0 = 0 

 

a. Assuming that a simple linear regression model is appro- priate, fit the regression model relating BOD (y) to the time (x). What is the estimate of o²? b. What is the estimate of expected BOD level when the time is 15 days? c. What change in mean BOD is expected when the time changes by 3 days? d. Suppose that the time used is 6 days. Calculate the fitted value of y and the corresponding residual. e. Calculate the fitted ŷ, for each value of x; used to fit the model. Then construct a graph of ŷ, versus the corresponding observed values y; and comment on what this plot would look like if the relationship between y and x was a deterministic (no random error) straight line. Does the plot actually obtained indicate that time is an effective regressor variable in pre- dicting BOD?
Transcribed Image Text:a. Assuming that a simple linear regression model is appro- priate, fit the regression model relating BOD (y) to the time (x). What is the estimate of o²? b. What is the estimate of expected BOD level when the time is 15 days? c. What change in mean BOD is expected when the time changes by 3 days? d. Suppose that the time used is 6 days. Calculate the fitted value of y and the corresponding residual. e. Calculate the fitted ŷ, for each value of x; used to fit the model. Then construct a graph of ŷ, versus the corresponding observed values y; and comment on what this plot would look like if the relationship between y and x was a deterministic (no random error) straight line. Does the plot actually obtained indicate that time is an effective regressor variable in pre- dicting BOD?
11.2.9 WP An article in the Journal of the Environmental Engineering Division ["Least Squares Estimates of BOD Param- eters" (1980, Vol. 106, pp. 1197-1202)] took a sample from the Holston River below Kingport, Tennessee, during August 1977. The biochemical oxygen demand (BOD) test is conducted over a period of time in days. The resulting data follow: Time (days): 1 2 4 68 10 12 14 16 18 20 BOD (mg/liter): 0.6 0.7 1.5 1.9 2.1 2.6 2.9 3.7 3.5 3.7 3.8
Transcribed Image Text:11.2.9 WP An article in the Journal of the Environmental Engineering Division ["Least Squares Estimates of BOD Param- eters" (1980, Vol. 106, pp. 1197-1202)] took a sample from the Holston River below Kingport, Tennessee, during August 1977. The biochemical oxygen demand (BOD) test is conducted over a period of time in days. The resulting data follow: Time (days): 1 2 4 68 10 12 14 16 18 20 BOD (mg/liter): 0.6 0.7 1.5 1.9 2.1 2.6 2.9 3.7 3.5 3.7 3.8
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