Homework 1
Danielle Moreno
Chapter 02 (page 54): 2, 5, 6, 8-10
Question 2
###Explain whether each scenario is a classification or regression problem, and indicate whether we are most interested in inference or prediction. Finally, provide n and p.
(a) We collect a set of data on the top 500 firms in the US. For each firm we record profit, number of employees, industry and the CEO salary. We are interested in understanding which factors affect CEO salary.
CEO Salary is a continuous variable, this is a regression problem. n=500 and p=3
Exercise 2.B
(b) We are considering launching a new product and wish to know whether it will be a success or a failure. We collect data on 20 similar products that were previously launched. For each product we have recorded whether it was a success or failure, price charged for the product, marketing budget, competition price, and ten other variables.
Succcess or failure is categorical therefore this is a classification problem. n=20 and p=13
Exercise 2.C
(c) We are interested in predicting the % change in the USD/Euro exchange rate in relation to the weekly changes in the world stock markets. Hence we collect weekly data for all of 2012. For each week we record the % change in the USD/Euro, the % change in the US market, the % change in the British market, and the % change in the German market.
Percent change is not categorical therefore is is a regression problem where n=52 and p=3.
Exercise 5
What are the advantages and disadvantages of a very flexible (versus a less flexible) approach for regression or classification? Under what circumstances might a more flexible approach be preferred to a less flexible approach? When might a less flexible approach be preferred?
Flexible Advantages:Can fit many different possible functional forms of f Disadvantages: Overfitting data. Can be difficult to understand the impact of individual predictors. Preferred: When we are only interested in prediction.
Less Flexible Preferred:If we are mainly interested in inference, then restrictive models are much more interpretable.
Exercise 6
Describe the differences between a parametric and a non-parametric statistical learning approach. What are the advantages of a parametric approach to regression or classification (as opposed to a nonparametric approach)? What are its disadvantages?
The parametric approach reduces the problem of estimating f down to one of estimating a set of parameters while Non-parametric methods do not make explicit assumptions about the functional form of f. Instead they seek an estimate of f that gets as close to the data points as possible without being too rough or wiggly.
The potential disadvantage of a parametric approach is that the model we choose will usually not match the true unknown form of f. If the chosen model is too far from the true f, then our estimate will be poor.
Advantage of non-parametric over parametric approach by avoiding the assumption of a particular functional form for f, they have the potential to accurately fit a wider range of possible shapes for f.
Disadvantage of non-parametric is it needs a large number of observationsto obtain an accurate estimate of f.
Exercise 8
This exercise relates to the College data set, which can be found in the file College.csv. It contains a number of variables for 777 different universities and colleges in the US.
(a) Use the read.csv() function to read the data into R. Call the loaded data college. Make sure that you have the directory set to the correct location for the data.
getwd()## [1] "C:/Users/danie/Desktop/STA Homework"college<-read.csv('College.csv')Exercise 8.b
(b) Look at the data using the fix() function. You should notice that the first column is just the name of each university. We don’t really want R to treat this as data. However, it may be handy to have these names for later. Try the following commands:
rownames(college)=college [,1]A cost of 1 results in the lowest cross-validation error.
##fix(college)college =college [,-1]##fix(college)Exercise 8.c
(c) Use the summary() function to produce a numerical summary of the variables in the data set.
summary(college)## Private Apps Accept Enroll
## Length:777 Min. : 81 Min. : 72 Min. : 35
## Class :character 1st Qu.: 776 1st Qu.: 604 1st Qu.: 242
## Mode :character Median : 1558 Median : 1110 Median : 434
## Mean : 3002 Mean : 2019 Mean : 780
## 3rd Qu.: 3624 3rd Qu.: 2424 3rd Qu.: 902
## Max. :48094 Max. :26330 Max. :6392
## Top10perc Top25perc F.Undergrad P.Undergrad
## Min. : 1.00 Min. : 9.0 Min. : 139 Min. : 1.0
## 1st Qu.:15.00 1st Qu.: 41.0 1st Qu.: 992 1st Qu.: 95.0
## Median :23.00 Median : 54.0 Median : 1707 Median : 353.0
## Mean :27.56 Mean : 55.8 Mean : 3700 Mean : 855.3
## 3rd Qu.:35.00 3rd Qu.: 69.0 3rd Qu.: 4005 3rd Qu.: 967.0
## Max. :96.00 Max. :100.0 Max. :31643 Max. :21836.0
## Outstate Room.Board Books Personal
## Min. : 2340 Min. :1780 Min. : 96.0 Min. : 250
## 1st Qu.: 7320 1st Qu.:3597 1st Qu.: 470.0 1st Qu.: 850
## Median : 9990 Median :4200 Median : 500.0 Median :1200
## Mean :10441 Mean :4358 Mean : 549.4 Mean :1341
## 3rd Qu.:12925 3rd Qu.:5050 3rd Qu.: 600.0 3rd Qu.:1700
## Max. :21700 Max. :8124 Max. :2340.0 Max. :6800
## PhD Terminal S.F.Ratio perc.alumni
## Min. : 8.00 Min. : 24.0 Min. : 2.50 Min. : 0.00
## 1st Qu.: 62.00 1st Qu.: 71.0 1st Qu.:11.50 1st Qu.:13.00
## Median : 75.00 Median : 82.0 Median :13.60 Median :21.00
## Mean : 72.66 Mean : 79.7 Mean :14.09 Mean :22.74
## 3rd Qu.: 85.00 3rd Qu.: 92.0 3rd Qu.:16.50 3rd Qu.:31.00
## Max. :103.00 Max. :100.0 Max. :39.80 Max. :64.00
## Expend Grad.Rate
## Min. : 3186 Min. : 10.00
## 1st Qu.: 6751 1st Qu.: 53.00
## Median : 8377 Median : 65.00
## Mean : 9660 Mean : 65.46
## 3rd Qu.:10830 3rd Qu.: 78.00
## Max. :56233 Max. :118.00ii. Use the pairs() function to produce a scatterplot matrix of the first ten columns or variables of the data. Recall that you can reference the first ten columns of a matrix A using A[,1:10].
## pairs(college[,1:10])iii. Use the plot() function to produce side-by-side boxplots of Outstate versus Private
boxplot(college$Outstate)
## iv. Create a new qualitative variable, called Elite, by binning the Top10perc variable. We are going to divide universities into two groups based on whether or not the proportion of students coming from the top 10 % of their high school classes exceeds 50 %.
Elite=rep("No",nrow(college ))
Elite[college$Top10perc >50]=" Yes"
Elite=as.factor(Elite)
college=data.frame(college , Elite)summary(college)## Private Apps Accept Enroll
## Length:777 Min. : 81 Min. : 72 Min. : 35
## Class :character 1st Qu.: 776 1st Qu.: 604 1st Qu.: 242
## Mode :character Median : 1558 Median : 1110 Median : 434
## Mean : 3002 Mean : 2019 Mean : 780
## 3rd Qu.: 3624 3rd Qu.: 2424 3rd Qu.: 902
## Max. :48094 Max. :26330 Max. :6392
## Top10perc Top25perc F.Undergrad P.Undergrad
## Min. : 1.00 Min. : 9.0 Min. : 139 Min. : 1.0
## 1st Qu.:15.00 1st Qu.: 41.0 1st Qu.: 992 1st Qu.: 95.0
## Median :23.00 Median : 54.0 Median : 1707 Median : 353.0
## Mean :27.56 Mean : 55.8 Mean : 3700 Mean : 855.3
## 3rd Qu.:35.00 3rd Qu.: 69.0 3rd Qu.: 4005 3rd Qu.: 967.0
## Max. :96.00 Max. :100.0 Max. :31643 Max. :21836.0
## Outstate Room.Board Books Personal
## Min. : 2340 Min. :1780 Min. : 96.0 Min. : 250
## 1st Qu.: 7320 1st Qu.:3597 1st Qu.: 470.0 1st Qu.: 850
## Median : 9990 Median :4200 Median : 500.0 Median :1200
## Mean :10441 Mean :4358 Mean : 549.4 Mean :1341
## 3rd Qu.:12925 3rd Qu.:5050 3rd Qu.: 600.0 3rd Qu.:1700
## Max. :21700 Max. :8124 Max. :2340.0 Max. :6800
## PhD Terminal S.F.Ratio perc.alumni
## Min. : 8.00 Min. : 24.0 Min. : 2.50 Min. : 0.00
## 1st Qu.: 62.00 1st Qu.: 71.0 1st Qu.:11.50 1st Qu.:13.00
## Median : 75.00 Median : 82.0 Median :13.60 Median :21.00
## Mean : 72.66 Mean : 79.7 Mean :14.09 Mean :22.74
## 3rd Qu.: 85.00 3rd Qu.: 92.0 3rd Qu.:16.50 3rd Qu.:31.00
## Max. :103.00 Max. :100.0 Max. :39.80 Max. :64.00
## Expend Grad.Rate Elite
## Min. : 3186 Min. : 10.00 Yes: 78
## 1st Qu.: 6751 1st Qu.: 53.00 No :699
## Median : 8377 Median : 65.00
## Mean : 9660 Mean : 65.46
## 3rd Qu.:10830 3rd Qu.: 78.00
## Max. :56233 Max. :118.00boxplot(college$Outstate, college$Elite)
v. Use the hist() function to produce some histograms with differing numbers of bins for a few of the quantitative variables. You may find the command par(mfrow=c(2,2)) useful: it will divide the print window into four regions so that four plots can be made simultaneously. Modifying the arguments to this function will divide the screen in other ways
par(mfrow = c(2,2))
hist(college$Books, col = 'red', xlab = "Books", ylab = "Count")
hist(college$PhD, col = 'yellow', xlab = "PhD", ylab = "Count")
hist(college$Accept, col = 'blue', xlab = "Accept", ylab = "Count")
hist(college$Enroll, col = 'green', xlab = "Enroll", ylab = "Count")
### vi. Continue exploring the data, and provide a brief summary of what you discover.
summary(college$Accept)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 72 604 1110 2019 2424 26330summary(college$Enroll)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 35 242 434 780 902 6392The data is interesting as looking at the histogram and summary both of these points are heavily skewed. I would make a transformation on this data to center it.
Question 9
TThis exercise involves the Auto data set studied in the lab. Make sure that the missing values have been removed from the data..
(a) Which of the predictors are quantitative, and which are qualitative?
auto <- read.csv("Auto.csv", na.strings = "?")
str(auto)## 'data.frame': 397 obs. of 9 variables:
## $ mpg : num 18 15 18 16 17 15 14 14 14 15 ...
## $ cylinders : int 8 8 8 8 8 8 8 8 8 8 ...
## $ displacement: num 307 350 318 304 302 429 454 440 455 390 ...
## $ horsepower : int 130 165 150 150 140 198 220 215 225 190 ...
## $ weight : int 3504 3693 3436 3433 3449 4341 4354 4312 4425 3850 ...
## $ acceleration: num 12 11.5 11 12 10.5 10 9 8.5 10 8.5 ...
## $ year : int 70 70 70 70 70 70 70 70 70 70 ...
## $ origin : int 1 1 1 1 1 1 1 1 1 1 ...
## $ name : chr "chevrolet chevelle malibu" "buick skylark 320" "plymouth satellite" "amc rebel sst" ...All variables except “horsepower” and “name” are quantitative.