ECON 491 - Applied Machine Learning in Economics
Problem Set 1 (50pts) - due date: Friday, September 2
Problem Set 1 (50pts) - due date: Friday, September 2
Yilun Zhang(yilun4)
02/09/2022
Question 1 (concept)[15p]
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 \(p\).
- 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.
- 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.
- 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.
Answer 1
- Because the predicted variables are numerical variables, this is a regression problem; We’re interested in understanding what factors affect CEO pay. It’s a matter of inference；n is 500, p is 3
- Since the question we are interested in is the success or failure of new products, it is a classification problem; We want to predict whether new products will succeed or fail. It’s a prediction problem. n is 20, p is 13
- Because we are interested in predicting the % change in the USD/Euro exchange rate in relation to the weekly changes in the world stock markets. The dependent variable is a numerical variable, so this is a regression problem; We need to forecast the dollar/euro exchange rate, so it’s a forecasting problem; n is 52, p is 3
Question 2 (applied)[35p for part (c)]
This exercise relates to the College data set, It contains a number of variables for 777 different universities and colleges in the US. The variables are
- Private: Public/private indicator
- Apps: Number of applications received
- Accept: Number of applicants accepted
- Enroll: Number of new students enrolled
- Top10perc: New students from top 10
- Top25perc: New students from top 25
- F.Undergrad: Number of full-time undergraduates
- P.Undergrad: Number of part-time undergraduates
- Outstate: Out-of-state tuition
- Room.Board: Room and board costs
- Books: Estimated book costs
- Personal: Estimated personal spending
- PhD: Percent of faculty with Ph.D.’s
- Terminal: Percent of faculty with terminal degree
- S.F.Ratio: Student/faculty ratio
- perc.alumni: Percent of alumni who donate
- Expend: Instructional expenditure per student
- Grad.Rate: Graduation rate
Before reading the data into R, it can be viewed in Excel or a text editor.
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. The R commands getwd() and setwd() may be helpful.
Look at the data using the View() 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:
You should see that there is now a row.names column with the name of each university recorded. This means that R has given each row a name corresponding to the appropriate university. R will not try to perform calculations on the row names. However, we still need to eliminate the first column in the data where the names are stored. Try
Now you should see that the first data column is Private. Note that another column labeled row.names now appears before the Private column. However, this is not a data column but rather the name that R is giving to each row.
- Use the summary() function to produce a numerical summary of the variables in the data set.
- 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].
- Use the plot() function to produce side-by-side boxplots of Outstate versus Private.
- 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%.
Use the summary() function to see how many elite universities there are. Now use the plot() function to produce side-by-side boxplots of Outstate versus Elite.
- 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.
- Continue exploring the data, and provide a brief summary of what you discover.
Answer 2 (applied)
For the applied questions all the written code needs to be provided, including the display. If you are going to display data (or large data.frames/matrices), please use the head() function in R to display just a small part of it.
college<- read.csv("C:\\Users\\Zhang Yilun\\Desktop\\College.csv")rownames(college) <- college[, 1]
college <- college[, -1]
head(college)## Private Apps Accept Enroll Top10perc Top25perc
## Abilene Christian University Yes 1660 1232 721 23 52
## Adelphi University Yes 2186 1924 512 16 29
## Adrian College Yes 1428 1097 336 22 50
## Agnes Scott College Yes 417 349 137 60 89
## Alaska Pacific University Yes 193 146 55 16 44
## Albertson College Yes 587 479 158 38 62
## F.Undergrad P.Undergrad Outstate Room.Board Books
## Abilene Christian University 2885 537 7440 3300 450
## Adelphi University 2683 1227 12280 6450 750
## Adrian College 1036 99 11250 3750 400
## Agnes Scott College 510 63 12960 5450 450
## Alaska Pacific University 249 869 7560 4120 800
## Albertson College 678 41 13500 3335 500
## Personal PhD Terminal S.F.Ratio perc.alumni Expend
## Abilene Christian University 2200 70 78 18.1 12 7041
## Adelphi University 1500 29 30 12.2 16 10527
## Adrian College 1165 53 66 12.9 30 8735
## Agnes Scott College 875 92 97 7.7 37 19016
## Alaska Pacific University 1500 76 72 11.9 2 10922
## Albertson College 675 67 73 9.4 11 9727
## Grad.Rate
## Abilene Christian University 60
## Adelphi University 56
## Adrian College 54
## Agnes Scott College 59
## Alaska Pacific University 15
## Albertson College 55summary(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. :118.00college$Private <- as.factor(college$Private)
pairs(college[,1:10])
plot(college$Private,college$Outstate)
Elite <- rep("No", nrow(college))
Elite[college$Top10perc > 50] <- "Yes"
Elite <- as.factor(Elite)
college <- data.frame(college, Elite)
summary(college$Elite)## No Yes
## 699 78plot(college$Elite,college$Outstate)
par(mfrow = c(2,2))
hist(college$Enroll)
hist(college$Accept)
hist(college$Books)
hist(college$PhD)
- As can be seen from the correlation coefficient figure, the variable Apps has a strong linear correlation with variable Accept. Likewise, the variable Enroll has a strong linear correlation with variable F.Nudergrad.
The variable Apps has a strong linear correlation with variable Enroll. There is a strong linear correlation between variable Accept and variable f.undergrad We verify our thinking by calculating the correlation coefficient
attach(college)## The following object is masked _by_ .GlobalEnv:
##
## Elitecor(Apps,Accept);cor(Enroll,F.Undergrad)## [1] 0.9434506## [1] 0.9646397cor(Apps,Enroll);cor(F.Undergrad,Accept)## [1] 0.8468221## [1] 0.8742233It can be seen from the calculation results of correlation coefficient that the variable Apps has a strong correlation with the variable Accept, and the correlation coefficient reaches 0.94.The correlation coefficient between the variable Enroll and F. Nudergrad reached 0.96. The correlation coefficient between Apps and Enroll was 0.85. The correlation coefficient between variable Accept and variable F.undergrad is 0.87 So there is a strong linear correlation between these variables