201122_Math217_Week12_RLab_Moneyball
Jerome
11/22/2020
getwd()## [1] "C:/Users/Jerome/Documents/From_Toshiba_HD_Work_Files/0000_Montgomery_College/Math_217/Week_12"download.file("http://www.openintro.org/stat/data/mlb11.RData", destfile = "mlb11.RData")
load("mlb11.RData")Exercise 1
plot(mlb11$hits~ mlb11$at_bats)
cor(mlb11$hits, mlb11$at_bats)## [1] 0.846472Exercise 2
The relationship is positive and fairly strong. There does appear to be a fairly wide distribution of scores. There are outliers at the higher end - players who either played many games in a shorter career or who played for an exceptional # of years.
plot_ss(x=mlb11$at_bats, y = mlb11$runs)
## Click two points to make a line.
## Call:
## lm(formula = y ~ x, data = pts)
##
## Coefficients:
## (Intercept) x
## -2789.2429 0.6305
##
## Sum of Squares: 123721.9plot_ss(x=mlb11$at_bats, y = mlb11$runs, showSquares = TRUE)
## Click two points to make a line.
## Call:
## lm(formula = y ~ x, data = pts)
##
## Coefficients:
## (Intercept) x
## -2789.2429 0.6305
##
## Sum of Squares: 123721.9Exercise 3
NB: My plot was not interactive. When I ran it the 1st time, it produced the line and gave me no option to choose. I had no option to choose after I displayed the squares.
m1 <- lm(runs ~ at_bats, data = mlb11)
summary(m1)##
## Call:
## lm(formula = runs ~ at_bats, data = mlb11)
##
## Residuals:
## Min 1Q Median 3Q Max
## -125.58 -47.05 -16.59 54.40 176.87
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2789.2429 853.6957 -3.267 0.002871 **
## at_bats 0.6305 0.1545 4.080 0.000339 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 66.47 on 28 degrees of freedom
## Multiple R-squared: 0.3729, Adjusted R-squared: 0.3505
## F-statistic: 16.65 on 1 and 28 DF, p-value: 0.0003388Exercise 4
plot(mlb11$runs ~ mlb11$at_bats)
plot(runs ~ at_bats, data = mlb11)
abline(m1)
Exercise 5
If a team has 5,578 at-bats, I would expect something over 700 runs, but < 750.
plot(m1$residuals ~ mlb11$at_bats)
abline(h = 0, lty = 3)
Exercise 6
I can’t see any pattern in the residuals, other than a kind of cluster (or 2) at the lower end of the abscissa, with a few outliers at the high end.
hist(m1$residuals)
qqnorm(m1$residuals)
qqline(m1$residuals)
Exercise 7
The distribution of the residuals appears to be nearly normal, but it is skewed to the right b/c of the outliers.
Exercise 8
Based on the m1 residuals plot in Exercise 6, it would seem the variability is constant, or nearly so.
On Your Own
m2 <- lm(runs ~ strikeouts, data = mlb11)
summary(m2)##
## Call:
## lm(formula = runs ~ strikeouts, data = mlb11)
##
## Residuals:
## Min 1Q Median 3Q Max
## -132.27 -46.95 -11.92 55.14 169.76
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1054.7342 151.7890 6.949 1.49e-07 ***
## strikeouts -0.3141 0.1315 -2.389 0.0239 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 76.5 on 28 degrees of freedom
## Multiple R-squared: 0.1694, Adjusted R-squared: 0.1397
## F-statistic: 5.709 on 1 and 28 DF, p-value: 0.02386plot(runs ~ strikeouts, data = mlb11)
abline(m2)
1.There is a weak linear relationship. Strikeouts do predict runs, in a sense. The more strikeouts, the fewer runs. But Babe Ruth’s record may give a different slant on this. From Wikipedia, “Ruth established many MLB batting (and some pitching) records, including career home runs (714), runs batted in (RBIs) (2,213), bases on balls (2,062), slugging percentage (. 690), and on-base plus slugging (OPS) (1.164); the last two still stand as of 2019.”
But Ruth also had a high strikeout percentage. “For many years, Babe Ruth was known as the King of Strikeouts. He was known for his all or nothing batting style. He led the American League in strikeouts five times and accumulated 1,330 of them in his career.” – This is from https://howtheyplay.com/team-sports/strikeouts-have-skyrocketed-since-Babe-Ruth#:~:text=For%20many%20years%2C%20Babe%20Ruth,of%20them%20in%20his%20career.
Ruth’s data were obviously not in this dataset; He would have been at 1300 on the abscissa and probably off the chart on the ordinate.
This R-squared value is R-squared: 0.1694; the at_bats R-squared was R-squared: 0.3729. In one sense, the at_bats is a better predictor, but since there is a strong inverse relationship w/ strikeouts (Ruth excepted), one could argue strikeouts is a good predictor.
Run 5 regressions
m3 <- lm(runs ~ hits, data = mlb11)
summary(m3)##
## Call:
## lm(formula = runs ~ hits, data = mlb11)
##
## Residuals:
## Min 1Q Median 3Q Max
## -103.718 -27.179 -5.233 19.322 140.693
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -375.5600 151.1806 -2.484 0.0192 *
## hits 0.7589 0.1071 7.085 1.04e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 50.23 on 28 degrees of freedom
## Multiple R-squared: 0.6419, Adjusted R-squared: 0.6292
## F-statistic: 50.2 on 1 and 28 DF, p-value: 1.043e-07m4 <- lm(runs ~ homeruns, data = mlb11)
summary(m4)##
## Call:
## lm(formula = runs ~ homeruns, data = mlb11)
##
## Residuals:
## Min 1Q Median 3Q Max
## -91.615 -33.410 3.231 24.292 104.631
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 415.2389 41.6779 9.963 1.04e-10 ***
## homeruns 1.8345 0.2677 6.854 1.90e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 51.29 on 28 degrees of freedom
## Multiple R-squared: 0.6266, Adjusted R-squared: 0.6132
## F-statistic: 46.98 on 1 and 28 DF, p-value: 1.9e-07m5 <- lm(runs ~ bat_avg, data = mlb11)
summary(m5)##
## Call:
## lm(formula = runs ~ bat_avg, data = mlb11)
##
## Residuals:
## Min 1Q Median 3Q Max
## -94.676 -26.303 -5.496 28.482 131.113
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -642.8 183.1 -3.511 0.00153 **
## bat_avg 5242.2 717.3 7.308 5.88e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 49.23 on 28 degrees of freedom
## Multiple R-squared: 0.6561, Adjusted R-squared: 0.6438
## F-statistic: 53.41 on 1 and 28 DF, p-value: 5.877e-08m6 <- lm(runs ~ stolen_bases, data = mlb11)
summary(m6)##
## Call:
## lm(formula = runs ~ stolen_bases, data = mlb11)
##
## Residuals:
## Min 1Q Median 3Q Max
## -139.94 -62.87 10.01 38.54 182.49
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 677.3074 58.9751 11.485 4.17e-12 ***
## stolen_bases 0.1491 0.5211 0.286 0.777
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 83.82 on 28 degrees of freedom
## Multiple R-squared: 0.002914, Adjusted R-squared: -0.0327
## F-statistic: 0.08183 on 1 and 28 DF, p-value: 0.7769m7 <- lm(runs ~ wins, data = mlb11)
summary(m7)##
## Call:
## lm(formula = runs ~ wins, data = mlb11)
##
## Residuals:
## Min 1Q Median 3Q Max
## -145.450 -47.506 -7.482 47.346 142.186
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 342.121 89.223 3.834 0.000654 ***
## wins 4.341 1.092 3.977 0.000447 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 67.1 on 28 degrees of freedom
## Multiple R-squared: 0.361, Adjusted R-squared: 0.3381
## F-statistic: 15.82 on 1 and 28 DF, p-value: 0.0004469plot(runs ~ bat_avg, data = mlb11)
abline(m5)
Batting Average wins, but not by much. Hits came a close 2nd, R-squared = 0.642; homeruns came in a close 3rd @ 0.627.
Call: lm(formula = runs ~ bat_avg, data = mlb11)
Residuals: Min 1Q Median 3Q Max -94.676 -26.303 -5.496 28.482 131.113
Coefficients: Estimate Std. Error t value Pr(>|t|)
(Intercept) -642.8 183.1 -3.511 0.00153 ** bat_avg 5242.2 717.3 7.308 5.88e-08 *** — Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 49.23 on 28 degrees of freedom Multiple R-squared: 0.6561, Adjusted R-squared: 0.6438 F-statistic: 53.41 on 1 and 28 DF, p-value: 5.877e-08
- Use New Variables
m8 <- lm(runs ~ new_onbase, data = mlb11)
summary(m8)##
## Call:
## lm(formula = runs ~ new_onbase, data = mlb11)
##
## Residuals:
## Min 1Q Median 3Q Max
## -58.270 -18.335 3.249 19.520 69.002
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1118.4 144.5 -7.741 1.97e-08 ***
## new_onbase 5654.3 450.5 12.552 5.12e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 32.61 on 28 degrees of freedom
## Multiple R-squared: 0.8491, Adjusted R-squared: 0.8437
## F-statistic: 157.6 on 1 and 28 DF, p-value: 5.116e-13m9 <- lm(runs ~ new_slug, data = mlb11)
summary(m9)##
## Call:
## lm(formula = runs ~ new_slug, data = mlb11)
##
## Residuals:
## Min 1Q Median 3Q Max
## -45.41 -18.66 -0.91 16.29 52.29
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -375.80 68.71 -5.47 7.70e-06 ***
## new_slug 2681.33 171.83 15.61 2.42e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 26.96 on 28 degrees of freedom
## Multiple R-squared: 0.8969, Adjusted R-squared: 0.8932
## F-statistic: 243.5 on 1 and 28 DF, p-value: 2.42e-15m10 <- lm(runs ~ new_obs, data = mlb11)
summary(m10)##
## Call:
## lm(formula = runs ~ new_obs, data = mlb11)
##
## Residuals:
## Min 1Q Median 3Q Max
## -43.456 -13.690 1.165 13.935 41.156
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -686.61 68.93 -9.962 1.05e-10 ***
## new_obs 1919.36 95.70 20.057 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 21.41 on 28 degrees of freedom
## Multiple R-squared: 0.9349, Adjusted R-squared: 0.9326
## F-statistic: 402.3 on 1 and 28 DF, p-value: < 2.2e-16plot(runs ~ new_obs, data = mlb11)
abline(m10)