The production of wine is a multibillion-dollar worldwide industry. In an attempt to develop a model of wine quality as judged by wine experts, data was collected from red wine variants of Portuguese "Vinho Verde" wine. (Data extracted from P. Cortez, Cerdeira, A., Almeida, F., Matos, T., and Reis, J., "Modeling Wine Preferences by Data Mining from Physiochemical Properties," Decision Support Systems, 47, 2009, pp. 547-553 and bit.ly/9xKlEa.) A sample of 50 wines is stored in Vinho Verde . Develop a simple linear regression model to predict wine quality, measured on a scale from 0 (very bad) to 10 (excellent), based on alcohol content (%).
a. Construct a scatter plot. For these data, b0 = -0.3529 and b1 = 0.5624.
b. Interpret the meaning of the slope, b1, in this problem.
c. Predict the mean wine quality for wines with a 10% alcohol content.
d. What conclusion can you reach based on the results of (a)-(c)?