## Linear Regression

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Introduction to linear regression

1.Choose another tradional variable from mlb11 that you think might be a good predictor

of runs. Produce a scaerplot of the two variables and t a linear model. At a glance, does there

seem to be a linear relaonship?

CODE:

predict_runs <- lm(runs ~ hits, data = mlb11)

predict_runs

plot(mlb11$runs ~ mlb11$hits)

abline(predict_runs)

plot(predict_runs$residuals ~ mlb11$hits)

abline(h = 0, lty = 3)

OUTPUT:

> predict_runs <- lm(runs ~ hits, data = mlb11)

> predict_runs

Call:

lm(formula = runs ~ hits, data = mlb11)

Coe#cients:

(Intercept) hits

-375.5600 0.7589

> plot(mlb11$runs ~ mlb11$hits)

> abline(predict_runs)

SCREENSHOT:

INFERENCE:

Yes, there seems to be a linear rela,onship between the two.

2. How does this relaonship compare to the relaonship between runs and at_bats? Use the

R2 values from the two model summaries to compare. Does your variable seem to

predict runs beer than at_bats? How can you tell?

CODE:

m1 <- lm(runs ~ at_bats, data = mlb11)

summary(m1)$r.squared

summary(predict_runs)$r.squared

OUTPUT:

> m1 <- lm(runs ~ at_bats, data = mlb11)

> summary(m1)$r.squared

[1] 0.3728654

> summary(predict_runs)$r.squared

[1] 0.6419388

SCREENSHOT:

INFERENCE:

The new model has a higher R^2 value and is far be8er than the previous model

3. Now that you can summarize the linear relaonship between two variables, invesgate the

relaonships between runs and each of the other ve tradional variables. Which variable best

predicts runs? Support your conclusion using the graphical and numerical methods we’ve

discussed (for the sake of conciseness, only include output for the best variable, not all ve).

CODE:

summary(lm(runs ~ at_bats, data = mlb11))$r.squared

summary(lm(runs ~ hits, data = mlb11))$r.squared

summary(lm(runs ~ wins, data = mlb11))$r.squared

summary(lm(runs ~ bat_avg, data = mlb11))$r.squared

m2<-lm(runs ~ bat_avg, data = mlb11)

plot(mlb11$runs ~ mlb11$bat_avg)

abline(m2)

OUTPUT:

> summary(lm(runs ~ at_bats, data = mlb11))$r.squared