Marketing a new cold medicine. A pharmaceutical company based in New Jersey recently introduced a new cold medicine called Coldex. (For proprietary reasons, the actual name of the product is withheld.) It is now sold in drugstores and supermarkets across the United States. Monthly sales for the first two years the product was on the market are reported in the next table. Consider the simple linear regression model, E(y_t) = β₀ + β₁t, where y_t is the sales in month t.

(a) Fit the simple linear model to the data. Is the model statistically useful for predicting monthly sales?

(b) Construct a plot of the regression residuals against month, t. Does the plot suggest the presence of residual correlation? Explain.

(c) Use the Durbin-Watson test to formally test for correlated errors.