The following correlation matrix shows the pairwise correlations among three variables. The variables are the expert ratings

The following correlation matrix shows the pairwise correlations among three variables. The variables are the €œexpert€ ratings assigned to wines by well-known connoisseurs (from 0 to 100), the year of the vintage (year in which the grapes were harvested), and the listed price on a Web site. For example, corr1year, price2 = 0.3222.

(a) Would a multiple regression of the ratings on year and price explain more than half of the variation in the ratings?
(b) If we regressed the standardized value of the rating (that is, subtract the mean rating and divide by the SD of the rating) on the standardized price (subtract the mean price and divide by the SD of the price), what would be the slope?
(c) Are the partial and marginal slopes for price identical? Explain.

Transcribed Image Text:

Rating Year Price Rating 1.0000 0.0966 0.7408 Year Price 0.0966 0 0.32222 0.7408 0.32222 1.00000