Thirty samples of cheddar cheese were examined for their content of acetic acid, hydrogen sulfide and lactic acid. Each sample was tased and scored by panel of judges and the average taste score produced. Use the cheddar data to answer the following questions. (Try help(cheddar) for information about the variables, and use cheddar to list the data.)
(a) Fit a regression model with taste as the response and the three chemical contents as predictors. Present a summary of your fitted model. (Use the R summary function.)
(b) Report the values of the regression coefficients.
(c) Identify the predictors that are statistically significant at the 5% level.
(d) Compute the correlation between the fitted values and the response. Square it. Identify where this value appears in the regression output.
(e) Fit the same regression model but without an intercept term. What is the value of R2 reported in the output? Is it equal to the squared correlation between fitted values and response for this model? Compute a more reasonable measure of the goodness of fit for this model.
(f) Compute 95% confidence intervals for all of the regression coefficients. (Use the full model.)