Please do it in R studio( install package\"alr4\" then load data file\"oldfaith\

Question

Please do it in R studio( install package"alr4" then load data file"oldfaith")! Please show code and work. In order to access to "oldfaith", it requires to install package"alr4" first.

J Ul less, and Ul larger number of words, Zipf's law J UICak down. Does that seem to happen with these data? 2.20 Old Faithful (Data file: oldfaith) Use the data from Problem 1.4. 2.20.1 Use simple linear regression methodology to obtain a prediction equation for interval from duration. Summarize your results in a way that might be useful for the nontechnical personnel who staff the Old Faithful Visitor's Center 2.20.2 An individual has just arrived at the end of an eruption that lasted 250 seconds. Give a 95% confidence interval for the time the individual will have to wait for the next eruption. 2.20.3 Estimate the 0.90 quantile of the conditional distribution of interval(duration = 250) assuming that the population is normally distributed.

Explanation / Answer

Programme: R

install.packages("alr4")

library(alr4)

df <- data.frame(oldfaith)

attach(df)

summary(df)

cor(df)

plot(df)

#Linear regression Interval Vs Duration

lr <- lm(Interval~Duration)

summary(lr)

#Duration =250 for prediciton

xd <- data.frame(Duration= c(250))

#applying prediciton for linear regression

predict(lr,xd, interval= "prediction")

#confidence interval=0.80

predict(lr,xd, interval = 'confidence', level = 0.80)

With output:

> summary(df)
Duration Interval
Min. : 96.0 Min. :43.00
1st Qu.:130.0 1st Qu.:58.00
Median :240.0 Median :76.00
Mean :209.9 Mean :71.11
3rd Qu.:267.8 3rd Qu.:82.00
Max. :306.0 Max. :96.00
> cor(df)
Duration Interval
Duration 1.0000000 0.8960697
Interval 0.8960697 1.0000000

> lr <- lm(Interval~Duration)
> summary(lr)

Call:
lm(formula = Interval ~ Duration)

Residuals:
Min 1Q Median 3Q Max
-12.3337 -4.5250 0.0612 3.7683 16.9722

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 33.987808 1.181217 28.77 <2e-16 ***
Duration 0.176863 0.005352 33.05 <2e-16 ***
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6.004 on 268 degrees of freedom
Multiple R-squared: 0.8029,   Adjusted R-squared: 0.8022
F-statistic: 1092 on 1 and 268 DF, p-value: < 2.2e-16

> xd <- data.frame(Duration= c(250))
> predict(lr,xd, interval= "prediction")
fit lwr upr
1 78.20354 66.35401 90.05307
> predict(lr,xd, interval = 'confidence', level = 0.80)
fit lwr upr
1 78.20354 77.65908 78.748

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