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5) Use the model'equation to predict the value of y using any x value of your choice within the given data range, use a value 0 .05. State the confidence limits and prediction limits. 6) Test the hypothesis Ho versus using a= 0.05. Find the P-value for this test and draw conclusion about the usefulness of the regression equation in Q2.

5) Use the model'equation to predict the value of y using any x value of your choice within the given data range, use a value 0 .05. State the confidence limits and prediction limits. 6) Test the hypothesis Ho versus using a= 0.05. Find the P-value for this test and draw conclusion about the usefulness of the regression equation in Q2.

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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The cetane number is a critical property in specifying the ignition quality of a fuel used in a diesel engine. Determination of this number for a biodiesel fuel is expensive and time-consuming. The article "Relating the Cetane Number of Biodiesel Fuels to Their Fatty Acid Composition: A Critical Study" (J. of Automobile Engr., 2009: 565–583) included the following data on x = iodine value (g) and y = cetane number for a sample of 15 biofuels The iodine value (x) is the amount of iodine necessary to saturate a sample of 100 g of oil. The article's authors fit the simple linear regression model to this data, so let s does the same. 132.0 129.0 120.0 113.2 105.0 92.0 84.0 88.4 59.0 80.0 81.0 81.5 71.0 69.2 63.0 y 46.0 48.0 51.0 52.1 54.0 52.0 59.0 58.7 61.6 64.0 61.4 54.6 58.8 58.0 51.4 Construct a scatter plot for the data. Identify and state which is dependent and independent variable. What is the purpose of the scatter plot/diagram? 2) Fit a simple linear regression line/ equation to your data. Give brief interpret about the regression analysis of the regression equation based on the printout and determine the R 2 also explain the coefficient of determination. 3) Estimate the correlation coefficient (Pearson coefficient), r, between x and y and explain briefly the strength of r and its direction and comment the p-value. 4) Construct a 95% two-sided confidence interval for the regression line. 5) Use the model'equation to predict the value of y using any x value of your choice within the given data range, use a value 0 .05. State the confidence limits and prediction limits. 6) Test the hypothesis Ho: versus using a = 0.05. Find the P-value for this test and draw conclusion about the usefulness of the regression equation in Q2. 7) Using the analysis of variance ANOVA output obtained from the print output calculate the coefficient of determination of the data and provide an interpretation of this quantity. State the null hypothesis and alternative hypothesis for the above model. Should the null
Transcribed Image Text:The cetane number is a critical property in specifying the ignition quality of a fuel used in a diesel engine. Determination of this number for a biodiesel fuel is expensive and time-consuming. The article "Relating the Cetane Number of Biodiesel Fuels to Their Fatty Acid Composition: A Critical Study" (J. of Automobile Engr., 2009: 565–583) included the following data on x = iodine value (g) and y = cetane number for a sample of 15 biofuels The iodine value (x) is the amount of iodine necessary to saturate a sample of 100 g of oil. The article's authors fit the simple linear regression model to this data, so let s does the same. 132.0 129.0 120.0 113.2 105.0 92.0 84.0 88.4 59.0 80.0 81.0 81.5 71.0 69.2 63.0 y 46.0 48.0 51.0 52.1 54.0 52.0 59.0 58.7 61.6 64.0 61.4 54.6 58.8 58.0 51.4 Construct a scatter plot for the data. Identify and state which is dependent and independent variable. What is the purpose of the scatter plot/diagram? 2) Fit a simple linear regression line/ equation to your data. Give brief interpret about the regression analysis of the regression equation based on the printout and determine the R 2 also explain the coefficient of determination. 3) Estimate the correlation coefficient (Pearson coefficient), r, between x and y and explain briefly the strength of r and its direction and comment the p-value. 4) Construct a 95% two-sided confidence interval for the regression line. 5) Use the model'equation to predict the value of y using any x value of your choice within the given data range, use a value 0 .05. State the confidence limits and prediction limits. 6) Test the hypothesis Ho: versus using a = 0.05. Find the P-value for this test and draw conclusion about the usefulness of the regression equation in Q2. 7) Using the analysis of variance ANOVA output obtained from the print output calculate the coefficient of determination of the data and provide an interpretation of this quantity. State the null hypothesis and alternative hypothesis for the above model. Should the null
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