Question

Exercise 2. [Data analysis, requires R] For this questions use the bac data set from the openintro library. To access this data set first install the package using install.packages ("openintro") (this only needs to be done once). Then load the pack- age into R with the command library(openintro). You can read about this data set in the help menu by entering the command ?openintro or help(openintro). Many people believe that gender, weight, drinking habits, and many other factors are much more important in predicting blood alcohol content (BAC) than simply considering the number of drinks a person consumed. Here we examine data from sixteen student volunteers at Ohio State University who each drank a randomly assigned number of cans of beer. These students were evenly divided between men and women, and they differed in weight and drinking habits. Thirty minutes later, a police officer measured their blood alcohol content (BAC) in grams of alcohol per deciliter of blood (a) Use the lm() function to fit a simple linear regression model with the BAC as the response variable and Beers (number of cans of beer) as the explanatory variable. Use the summary () function to print the results (b) Make a scatter plot with BAC on the y-axis and Beers on the x-axis. Add the least squares line. (c) Interpret the slope and the intercept in context (d) Interpret that R2 (coefficient of determination) (e) Calculate a 95% confidence interval for A and A [hint: use conf int(). Is 0 a plausible value for the intercept Bo? (f) What is the predicted BAC for a person that drank 4 cans of beer. Also, calculate a 95% prediction interval for the BAC of a person that drank 4 cans of beer. Is 0.08 a plausible BAC for a person that drank 4 cans of beer?

Answer 1

library(openintro)
Bac=bac$BAC
beers=bac$Beers

#part a
fit=lm(Bac~beers)
summary(fit)

#part b
plot(beers,Bac,main="scatter plot of Beers on BAC")
abline(a=fit$coefficients[1],b=fit$coefficients[2])

#part c
#interpritaion: here intrcept is -0.0127 that means when effect of beers
#is zero then BAC will be at negative -0.0127
#here slope is 0.01796376 means, increasing of one unit in Beers
#BAC will increase 0.01796376 times.

#part d
# in Regression we ger R-squared: 0.7998,
# this means 79.98% of variablity of BAC is explained by Beers.

scatter plot of Beers on BAC 4 6 beers