A chemical plant measures the mass of a reactant, xxx (in units of 10 kg), and the resulting yield of a purified catalyst, yyy (in decigrams), for a random sample of 12 batches. The data are summarised as follows:
∑x=360∑x2=12000∑y=144∑y2=1928 \sum x = 360 \quad \sum x^2 = 12000 \quad \sum y = 144 \quad \sum y^2 = 1928 ∑x=360∑x2=12000∑y=144∑y2=1928and the regression line of yyy on xxx has equation y=1.5+0.35xy = 1.5 + 0.35xy=1.5+0.35x.
Use the regression line to estimate the yield in grams for a batch using 470 kg of reactant.
Find SyyS_{yy}Syy and SxxS_{xx}Sxx.
Calculate the product moment correlation coefficient between yyy and xxx.
An 13th batch is added to the sample. It involves 300 kg of reactant and a yield of 1.525 grams of catalyst.
Use the formula Sxy=∑(x−xˉ)(y−yˉ)S_{xy} = \sum (x - \bar{x})(y - \bar{y})Sxy=∑(x−xˉ)(y−yˉ) to show that the value of SxyS_{xy}Sxy for the 13 batches will be the same as it was for the original 12 batches.
Find the new equation of the regression line of yyy on xxx for the 13 batches.
Comment on the suitability of using the new regression line to estimate the yield for a batch using 1800 kg of reactant. Provide a reason for your answer.
