In Class Activity #8

Exercise 1

If a baseball team’s OBP is 0.361 and SLG is 0.409, how many runs do we expect the team to score?

Using the linear regression model constructed during the lecture (the one that uses OBP and SLG as independent variables), find the number of runs we expect the team to score:

runsScoredModel <- lm(RS ~ OBP + SLG, data = baseball)
summary(runsScoredModel)

Call:
lm(formula = RS ~ OBP + SLG, data = baseball)

Residuals:
    Min      1Q  Median      3Q     Max 
-78.365 -16.821  -1.208  16.477  92.684 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -811.66      16.75  -48.47   <2e-16 ***
OBP          2830.70      77.94   36.32   <2e-16 ***
SLG          1517.58      35.17   43.15   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 25.12 on 1229 degrees of freedom
Multiple R-squared:  0.9248,    Adjusted R-squared:  0.9247 
F-statistic:  7557 on 2 and 1229 DF,  p-value: < 2.2e-16

newTeamOffense <- data.frame(OBP = 0.361, SLG = 0.409)
predict(runsScoredModel, newdata = newTeamOffense)

       1 
830.9116 

Exercise 2

If a baseball team’s opponents OBP (OOBP) is 0.267 and opponents SLG (OSLG) is 0.392, how many runs do we expect the team to allow?

Using the linear regression model discussed during the lecture (the one on the last slide of the previous video), find the number of runs we expect the team to allow.

runsAllowedModel <- lm(RA ~ OOBP + OSLG, data = baseball)
summary(runsAllowedModel)

Call:
lm(formula = RA ~ OOBP + OSLG, data = baseball)

Residuals:
    Min      1Q  Median      3Q     Max 
-76.805 -18.208   0.146  19.706  72.286 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -877.61      29.36  -29.89   <2e-16 ***
OOBP         2864.60     156.04   18.36   <2e-16 ***
OSLG         1632.76      90.03   18.14   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 27.18 on 417 degrees of freedom
  (812 observations deleted due to missingness)
Multiple R-squared:  0.9042,    Adjusted R-squared:  0.9038 
F-statistic:  1969 on 2 and 417 DF,  p-value: < 2.2e-16

newTeamDefense <- data.frame(OOBP = 0.267, OSLG = 0.392)
predict(runsAllowedModel, newdata = newTeamDefense)

       1 
527.2847 

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