Static question
Problem 2
The production of wine is a multi-billion-dollar worldwide industry. In an attempt to develop a model of wine quality as judged by wine experts, data (see Excel file VinhoVerde) was collected from red wine variants from a particular type of foreign wine. A multiple linear regression model should be developed from a sample of several wines. The model will be used to predict wine quality, measured on a scale from 0 (very bad) to 10 (excellent) based on the alcohol content (%) and the amount of chlorides.
- a) State the multiple linear regression equation with the number of independent variables related to the problem in general.
- b) Run the Regression Data analysis on this data, provide the obtained model.
- c) Interpret the meaning of the parameters β1 and β2 of the model (what does each of them represent?). Does β0 have a practical interpretation?
- d) Predict the mean wine quality rating for wines with
(i) 11% alcohol content and chlorides of 0.07.
(ii) 40% alcohol content and chlorides of 0.08.
Comment on whether the model is suitable for the requested predictions.
- e) Test the hypothesis on whether the slopes of the model are (jointly) significant.
- f) Test the hypothesis on whether each variable in the model (individually) is significant.
- g) In case when you find in (e)-(f) that some parameter of the model is insignificant, delete it from the model and run your new model.
