Astringency is the quality in a wine that makes the wine drinker’s mouth feel slightly rough, dry, and puckery. The paper “Analysis of Tannins in Red Wine Using Multiple Methods: Correlation with Perceived Astringency” (Amer. J.

of Enol. and Vitic., 2006: 481–485) reported on an investigation to assess the relationship between perceived astringency and tannin concentration using various analytic methods. Here is data provided by the authors on x tannin concentration by protein precipitation and y perceived astringency as determined by a panel of tasters Relevant summary quantities are as follows:

a. Fit the simple linear regression model to this data. Then determine the proportion of observed variation in 5 3.83071088 Sxy 5 3.497811 2 (19.404)(2.549)/32 Syy 5 11.82637622 Sxx 5 13.248032 2 (19.404)2 /32 5 1.48193150, gy2 i 5 11.835795, gxi yi 5 3.497811 gxi 5 19.404, gyi 5 2.549, gxi 2 5 13.248032, astringency that can be attributed to the model relationship between astringency and tannin concentration.

b. Calculate and interpret a confidence interval for the slope of the true regression line.

c. Estimate true average astringency when tannin concentration is .6, and do so in a way that conveys information about reliability and precision.

d. Predict astringency for a single wine sample whose tannin concentration is .6, and do so in a way that conveys information about reliability and precision.

e. Does it appear that true average astringency for a tannin concentration of .7 is something other than 0? State and test the appropriate hypotheses.