Linear Regression models can be used to predict Ty Cobb's Expected true yearly batting averages from his observed yearly "batavg" and the 5 other variables stored in the "tycobb" data.frame. Predictions from such "models" can address the question: "Was Ty Cobb ever a TRUE .400 hitter?" Since a player's seasonal batavg is a "random variable," the fact that Cobb's batavg was 0.4196 in 1911 and 0.4105 in 1912 does not necessarily imply that his Expected Seasonal batavg was truly over .400 in either of those consecutive seasons. For example, his batavg was 0.4011 in 1922 (10 years later). However, his seasonal batavg had dipped to "only" 0.3341 in 1920.
"Cobb lived off the field as though he wished to live forever. He lived on the field as though it was his last day." -- Branch Rickey, Major League Baseball Hall of Fame executive.
data(tycobb)A data frame with 24 observations (years) on the following 6 variables.
yearTy Cobb's 24 American League Seasons: 1905 - 1928.
hitsTotal number of Hits that season.
atbatsTotal number of times at Bat that season.
CMsplCarl Morris' Piecewise-Linear Spline term with "knot" in season 6 (1910).
seasonsLinear "Trend" term: 1, 2, ..., 24.
batavgCobb's Seasonal Batting Average ... 7 decimal places.
Carl Morris. (1982). "Was Ty Cobb ever a TRUE .400 hitter?" One-page Handout for his JSM Lecture on August 18 in Cincinnati, Ohio.