At a hydrocarbon processing factory, process control involves periodic analysis of samples for a certain process quality parameter. The analytic procedure currently used is costly and time consuming. A faster and more economical alternative procedure has been proposed. However, the numbers for the quality parameter given by the alternative procedure are somewhat different from those given by the current procedure, not because of any inherent errors but because of changes in the nature of the chemical analysis. Management believes that if the numbers from the new procedure can be used to forecast reliably the corresponding numbers from the current procedure, switching to the new procedure would be reasonable and cost effective. The following data were obtained for the quality parameter by analyzing samples using both procedures: Current (Y) Proposed (X) Proposed (X) Current (Y) 3.0 3.1 3.8 2.9 3.5 3.3 ITTI 4.0 2.9 3.7 2.1 3.6 3.2 3.7 2.8 2.9 3.0 3.3 3.6 4.0 2.7 3.1 (Enter your response rounded to three decimal places.) (Enter your response rounded to three decimal places.) (Enter your response rounded to three decimal places.) 3.1 The increases in X mostly result in how closely the data on the dependent variable cluster around the 3.0 3.6 4.2 2.6 3.0 a. Use linear regression to find a relation to forecast Y, which is the quality parameter from the current procedure, using the values from the proposed procedure, X. The forecasting model is given by the equation Y=+x. (Enter your responses rounded to three decimal places.) b. Is there a strong relationship between Y and X? Explain. The correlation coefficient, r, is The coefficient of determination, r2, is The standard error of estimate is 2.7 in Y. Also,% of the variation in Y is explained by X. The obtained value of the standard error of estimate, in turn, measures ▼ (Enter your response rounded to one decimal place.)
At a hydrocarbon processing factory, process control involves periodic analysis of samples for a certain process quality parameter. The analytic procedure currently used is costly and time consuming. A faster and more economical alternative procedure has been proposed. However, the numbers for the quality parameter given by the alternative procedure are somewhat different from those given by the current procedure, not because of any inherent errors but because of changes in the nature of the chemical analysis. Management believes that if the numbers from the new procedure can be used to forecast reliably the corresponding numbers from the current procedure, switching to the new procedure would be reasonable and cost effective. The following data were obtained for the quality parameter by analyzing samples using both procedures: Current (Y) Proposed (X) Proposed (X) Current (Y) 3.0 3.1 3.8 2.9 3.5 3.3 ITTI 4.0 2.9 3.7 2.1 3.6 3.2 3.7 2.8 2.9 3.0 3.3 3.6 4.0 2.7 3.1 (Enter your response rounded to three decimal places.) (Enter your response rounded to three decimal places.) (Enter your response rounded to three decimal places.) 3.1 The increases in X mostly result in how closely the data on the dependent variable cluster around the 3.0 3.6 4.2 2.6 3.0 a. Use linear regression to find a relation to forecast Y, which is the quality parameter from the current procedure, using the values from the proposed procedure, X. The forecasting model is given by the equation Y=+x. (Enter your responses rounded to three decimal places.) b. Is there a strong relationship between Y and X? Explain. The correlation coefficient, r, is The coefficient of determination, r2, is The standard error of estimate is 2.7 in Y. Also,% of the variation in Y is explained by X. The obtained value of the standard error of estimate, in turn, measures ▼ (Enter your response rounded to one decimal place.)
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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Transcribed Image Text:At a hydrocarbon processing factory, process control involves periodic analysis of samples for a certain process quality parameter. The analytic procedure currently used is
costly and time consuming. A faster and more economical alternative procedure has been proposed. However, the numbers for the quality parameter given by the alternative
procedure are somewhat different from those given by the current procedure, not because of any inherent errors but because of changes in the nature of the chemical
analysis.
Management believes that if the numbers from the new procedure can be used to forecast reliably the corresponding numbers from the current procedure, switching to the
new procedure would be reasonable and cost effective. The following data were obtained for the quality parameter by analyzing samples using both procedures:
Current (Y)
2.9
3.0
3.3
3.6
4.0
2.7
3.1
Proposed (X)
3.0
3.8
3.5
4.0
3.7
3.6
3.7
Current (Y)
3.1
2.9
3.3
2.9
2.1
3.2
2.8
The increases in X mostly result in
how closely the data on the dependent variable cluster around the
a. Use linear regression to find a relation to forecast Y, which is the quality parameter from the current procedure, using the values from the proposed procedure, X.
The forecasting model is given by the equation Y =
+ x. (Enter your responses rounded to three decimal places.)
b. Is there a strong relationship between Y and X? Explain.
The correlation coefficient, r, is
The coefficient of determination, r², is
(Enter your response rounded to three decimal places.)
(Enter your response rounded to three decimal places.)
The standard error of estimate is. (Enter your response rounded to three decimal places.)
Proposed (X)
3.1
3.0
3.6
4.2
2.6
3.0
2.7
in Y. Also,% of the variation in Y is explained by X. The obtained value of the standard error of estimate, in turn, measures
(Enter your response rounded to one decimal place.)
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