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. Automobile Engr. 2009: 565–583) included the following data on x = iodine value (g) and y = cetane number for a sample of 14 biofuels. The iodine value 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 follow their lead.

a. Obtain the equation of the least squares line, and then calculate a point prediction of the cetane number that would result from a single observation with an iodine value of 100.
b. Calculate and interpret the coefficient of determination.
c. Calculate and interpret a point estimate of the model standard deviation σ.

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X y X y 132.0 129.0 120.0 113.2 105.0 46.0 48.0 51.0 52.1 54.0 83.2 58.7 88.4 59.0 61.6 64.0 80.0 81.5 61.4 54.6 92.0 52.0 84.0 59.0 71.0 69.2 58.8 58.0