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Staff members of an oil refinery believe that the octane reading of a particular petrol depends on one of its raw materials. A sample of the related raw material (x) and octane number (y) was collected and the measurements below were found. El-1 x = 401.90 E-, x? = 23,126.35 El-1y = 644.00 E-1y² = 59,254.08 El-1 xi y = 36,966,83 i) Estimate and interpret a fitted linear regression model for the data collected. ii) Test the hypotheses Ho : B1 = 0 versus H, : B1 # 0 at a 10% level of significance. Include a p-value in your test. iii) Construct a 90% confidence interval for the estimated intercept of the linear regression model.

Staff members of an oil refinery believe that the octane reading of a particular petrol depends on one of its raw materials. A sample of the related raw material (x) and octane number (y) was collected and the measurements below were found. El-1 x = 401.90 E-, x? = 23,126.35 El-1y = 644.00 E-1y² = 59,254.08 El-1 xi y = 36,966,83 i) Estimate and interpret a fitted linear regression model for the data collected. ii) Test the hypotheses Ho : B1 = 0 versus H, : B1 # 0 at a 10% level of significance. Include a p-value in your test. iii) Construct a 90% confidence interval for the estimated intercept of the linear regression model.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Staff members of an oil refinery believe that the octane reading of a particular petrol depends on one of its raw materials. A sample of the related raw material (x) and octane number (y) was collected and the measurements below were found. E-1 X = 401.90 E-1 x;? = 23,126,35 El-1 yi = 644.00 El-1y? = 59,254.08 El-1 Xi Yi = 36,966.83 i) Estimate and interpret a fitted linear regression model for the data collected. ii) Test the hypotheses Ho : B1 = 0 versus H : B1 # 0 at a 10% level of significance. Include a p-value in your test. ii) Construct a 90% confidence interval for the estimated intercept of the linear regression model. iv) Conduct an F test at a = 0.10, to determine whether the regression model obtained in (i) is significant. v) Calculate and interpret the coefficient of determination, R². Using this value, determine whether the regression model adequate. vi) Suppose that another regression model was constructed from a similar data set where its adjusted R2 was found to be R2 = 0.107. Is this model better than our current model? Why? Show working to support your answer.
Transcribed Image Text:Staff members of an oil refinery believe that the octane reading of a particular petrol depends on one of its raw materials. A sample of the related raw material (x) and octane number (y) was collected and the measurements below were found. E-1 X = 401.90 E-1 x;? = 23,126,35 El-1 yi = 644.00 El-1y? = 59,254.08 El-1 Xi Yi = 36,966.83 i) Estimate and interpret a fitted linear regression model for the data collected. ii) Test the hypotheses Ho : B1 = 0 versus H : B1 # 0 at a 10% level of significance. Include a p-value in your test. ii) Construct a 90% confidence interval for the estimated intercept of the linear regression model. iv) Conduct an F test at a = 0.10, to determine whether the regression model obtained in (i) is significant. v) Calculate and interpret the coefficient of determination, R². Using this value, determine whether the regression model adequate. vi) Suppose that another regression model was constructed from a similar data set where its adjusted R2 was found to be R2 = 0.107. Is this model better than our current model? Why? Show working to support your answer.
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