Bsad Lab09
CME Group Foundation Business Analytics Lab
Ahad Sami
4/17/2019
About
The best way to create a predictive model is to begin with a complete data set. Split the data into two seperate datasets: the training set and the testing set, with the training set greater than or equal to 50% of the data. We will use the training set to build a model best predictor of the data. Lastly, we will test the built model on the testing data set, and assess how good the model is in predicting the actual values.
The concept may seem overwhelming, but we already have almost all of the tools to perform this analysis.
Setup
Remember to always set your working directory to the source file location. Go to ‘Session’, scroll down to ‘Set Working Directory’, and click ‘To Source File Location’. Read carefully the below and follow the instructions to complete the tasks and answer any questions. Submit your work to RPubs as detailed in previous notes.
Note
For your assignment you may be using different data sets than what is included here. Always read carefully the instructions on Sakai. Tasks/questions to be completed/answered are highlighted in larger bolded fonts and numbered according to their particular placement in the task section.
PART A: TRAINING SET & MODEL BUILDING
The first half of this lab focus on building a model using the training data. The data we will be using was obtained from Kaggle site[1] and is in reference to world university rankings [2] . The data looks at university world scoring based on different ranking criteria such as rank for quality of education, rank for quality of faculty, and rank for patents. We begin by reading the training data set ‘universityrank_training.csv’ file, and checking the header lines to make sure the data is read correctly.
traindata = read.csv(file="data/universityrank_training.csv", header=TRUE)
head(traindata)## world_rank institution country
## 1 1 Harvard University USA
## 2 2 Massachusetts Institute of Technology USA
## 3 3 Stanford University USA
## 4 4 University of Cambridge United Kingdom
## 5 5 California Institute of Technology USA
## 6 6 Princeton University USA
## national_rank quality_of_education alumni_employment quality_of_faculty
## 1 1 7 9 1
## 2 2 9 17 3
## 3 3 17 11 5
## 4 1 10 24 4
## 5 4 2 29 7
## 6 5 8 14 2
## publications influence citations broad_impact patents score year
## 1 1 1 1 NA 5 100.00 2012
## 2 12 4 4 NA 1 91.67 2012
## 3 4 2 2 NA 15 89.50 2012
## 4 16 16 11 NA 50 86.17 2012
## 5 37 22 22 NA 18 85.21 2012
## 6 53 33 26 NA 101 82.50 2012Next, we extract the two columns of interest and call them properly so we can easily refer to them later in the code.
patent_train = traindata$patents
score_train = traindata$scoreThe first model we will build is a simple linear model and we also plot the patents versus the score data. We will use the patents ranking variable to predict the university score. To better understand the data, the lower the patents ranking number the better it is. A value of 1 is a top rank for patents and represent the highest category in terms of number of patents owned by the particular academic institution. On the other hand the higher the calculated total score the better, as reflected by the world rank number. A value of 100 is a perfect score.
linear_train = lm(score_train ~ patent_train)
summary(linear_train)##
## Call:
## lm(formula = score_train ~ patent_train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.876 -4.014 -1.121 1.515 45.470
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 54.6406641 0.3859848 141.56 <2e-16 ***
## patent_train -0.0157607 0.0008291 -19.01 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.539 on 1197 degrees of freedom
## Multiple R-squared: 0.2319, Adjusted R-squared: 0.2313
## F-statistic: 361.4 on 1 and 1197 DF, p-value: < 2.2e-16plot(patent_train,score_train)
abline(linear_train, col="blue", lwd=2)
##### Consider now building a non-linear quadratic model. Follow the steps in lab07 to derive a quadratic model similar to what we did for costs versus servers. #### TASK 1: First, define a new variable patent_train2 which is the squared value of patent_train (defined above)
patent_train2 = patent_train^2TASK 2: Second, derive the quadratic regression model to predict the score_train from patent_train. You may want to call it quad_train.
quad_train = lm(score_train ~ patent_train + patent_train2)TASK 3: Third, publish the summary statistics.
summary(quad_train)##
## Call:
## lm(formula = score_train ~ patent_train + patent_train2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.556 -2.347 -0.578 1.301 40.842
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.966e+01 4.973e-01 119.97 <2e-16 ***
## patent_train -6.250e-02 3.321e-03 -18.82 <2e-16 ***
## patent_train2 5.975e-05 4.130e-06 14.47 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.957 on 1196 degrees of freedom
## Multiple R-squared: 0.3463, Adjusted R-squared: 0.3452
## F-statistic: 316.8 on 2 and 1196 DF, p-value: < 2.2e-16TASK 4: Based on the values of R-Squared and Adj R-Squared for both the linear and the quadratic select the best predictive model. Explain your argument.
ANSWER TASK 4:
According to the adjusted R-squared, the quadratic model is the best predictive model because it has the higher adjusted R-squared value as compared with the linear.
PART B: TESTING SET & MODEL EVALUATION
The second half of predictive modeling is about testing the model using a different data set called the testing data. Again we must first read the testing data set, and make sure the dataset is read propertly.
testdata = read.csv("data/universityrank_testing.csv", header=TRUE)
head(testdata)## world_rank institution country
## 1 1000 Yanbian University China
## 2 1 Harvard University USA
## 3 2 Stanford University USA
## 4 3 Massachusetts Institute of Technology USA
## 5 4 University of Cambridge United Kingdom
## 6 5 University of Oxford United Kingdom
## national_rank quality_of_education alumni_employment quality_of_faculty
## 1 84 355 478 210
## 2 1 1 1 1
## 3 2 9 2 4
## 4 3 3 11 2
## 5 1 2 10 5
## 6 2 7 13 10
## publications influence citations broad_impact patents score year
## 1 890 790 800 1000 737 44.18 2014
## 2 1 1 1 1 3 100.00 2015
## 3 5 3 3 4 10 98.66 2015
## 4 15 2 2 2 1 97.54 2015
## 5 11 6 12 13 48 96.81 2015
## 6 7 12 7 9 15 96.46 2015We extract again the two columns of interest, in reference this time to the testing data set, and call them accordingly.
patent_test = testdata$patents
score_test = testdata$scoreWe are ready now to check if the derived models are actually good predictive models. First we calculate the predicted test data score using the linear models derived earlier.
# Calculate the predicted score for the linear model (built in Part A) run on the patent_test data
score_predict1 = coef(linear_train)[1] + coef(linear_train)[2]*patent_testFor a visual representation we can plot the actual testing data, and overlay the predicted values
# Plot the actual values for patent and score as observed in the testing data set
plot(patent_test, score_test, main='Test Data -- Score vs Patent')
# Overlay the predicted values as calculated from the linear model and derived using the training model. The red color is used to distinguish the predicted values which, because of the linear model, will fit exactly a line
par(new=TRUE, xaxt="n", yaxt="n", ann=FALSE)
plot(patent_test, score_predict1, col="red")
A better way to qualify the goodness of a predictive model is to scatter plot the actual values against the predicted values. In a perfect predictive model the points will line up along the diagonal line. This is rarely the case, if ever!
#Plot predicted values from the linear model versus actual values form the test data
plot(score_test, score_predict1, xlab='Actual', ylab='Predict', main='Linear Model -- Predict vs Actual Test')
From the plot we can easily see that most of the predicted values versus actual are far from the diagoonal line. In many cases this is fine. Finally, to quantify the goodness of a model, we need to calculate the Root Mean Square Error (RMSE) and we name the variable as rmse1.
#Calculate RMSE for Linear Model
error1 = sum((score_predict1 - score_test)^2)/length(score_test)
rmse1 = sqrt(error1)
rmse1## [1] 5.956123It is hard to judge the goodness of the number unless we compare to other possibilities. Of course a perfect scenario will have zero RMSE. We now need to repeat the above calculations for the non-linear quadratic model.
Start by calculating the predicted values and overlay the calculated predicted values over the actual values.
TASK 5: Calculate score_predict2 based on the quadratic model and the patent test data. You need to refer again to the coefficients of the quadratic model derived earlier and the actual patent values obtained from the testing data.
score_predict2 = coef(quad_train)[1] + coef(quad_train)[2]*patent_test + coef(quad_train)[3]*patent_test^2For a visual representation, similar to the linear model, we need to do the following.
TASK 6: Plot the score versus patent actual test data and overlay the predictied values as calculated in TASK 5.
# TASK 6A: Plot the actual values for patent and score as observed in the testing data set. Write the code below:
plot(patent_test, score_test, main='Test Data -- Score vs Patent')
# Overlay the predicted values as calculated from the quadratic model and derived using the training model.The GREEN color is used to distinguish the predicted values which, because of the quadratic model, will in this case fit exactly a parabola.
# TASK 6B: Write the code below the following code.
par(new=TRUE, xaxt="n", yaxt="n", ann=FALSE)
plot(patent_test, score_predict2, col="green")
#### TASK 7: Plot the predicted values against the true values. Label properly.
Plot the predicted values form the quadratic model versus the actual values from the test data. Write the code below:
plot(score_test, score_predict2, xlab='Actual', ylab='Predict', main='Quadratic Model -- Predict vs Actual Test')
TASK 8: By looking at the scatterplots for the linear and quadratic models are you able to tell which model is better? Elaborate.
ANSWER TASK 8:
According to the two models, the quadratic models are better because they have mored data clustered in the lower left corner which means it is closer to the diagonal line than in the linear model.
A better way to quantify the goodness of the model is to calculate again the RMSE.
TASK 9: Calculate the root mean square error (RMSE) for the quadratic model.
#Calculate RMSE for Quadratic Model. Write the code below and name the variable as rmse2:
error2 = sum((score_predict2 - score_test)^2)/length(score_test)
rmse2 = sqrt(error2)
rmse2## [1] 5.684821TASK 10: Based on the root mean square error (RMSE) which model is better? How do results reconcile with the results from Task 4?
ANSWER TASK 10:
The linear model’s rmse is 5.956 and the quadratic model’s is 5.685
Based on the rmse, the quadratic model is better. This result relates to task 4 that the quadratic model has a highder adjusted r-squared, deeming it better than the linear model in terms of correlation.
source [1]: http://www.kaggle.com source [2]: http://www.cwur.org