8) What are the assumptions of a simple linear regression model.

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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.
x 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
у 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
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
hypothesis be rejected?
8) What are the assumptions of a simple linear regression model.
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. x 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 у 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 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 hypothesis be rejected? 8) What are the assumptions of a simple linear regression model.
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