Utilizing Supervised Learning in Learning Analytics

Case Study 4

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Business Scenario: Predicting Student Performance

In this case study, you are an analyst at an online education platform. The management is interested in predicting student performance based on various factors to provide personalized support and improve the learning experience. Your task is to develop a supervised learning model to predict students’ final grades using simulated data.

Objective:

Your goal is to build a predictive model using supervised learning techniques in R. You will utilize simulated student data with features such as study hours, quiz scores, forum participation, and previous grades to predict the final grades.

Data Generation:

# Set a fixed random seed for reproducibility
set.seed(10923)


# Number of students
#TODO: set num_students to 500
# Enter code below:
num_students = 500


# Simulate study hours (ranging from 1 to 20 hours)
study_hours <- sample(1:20, num_students, replace = TRUE)

# Simulate quiz scores (ranging from 0 to 100)
quiz_scores <- sample(0:100, num_students, replace = TRUE)

# Simulate forum participation (ranging from 0 to 50 posts)
forum_posts <- sample(0:50, num_students, replace = TRUE)

# Simulate previous grades (ranging from 0 to 100)
previous_grades <- sample(0:100, num_students, replace = TRUE)

# Simulate final grades (ranging from 0 to 100)
final_grades <- 0.3 * study_hours + 0.4 * quiz_scores + 0.2 * forum_posts + 0.1 * previous_grades + rnorm(num_students, mean = 0, sd = 5) + 25

# Create a data frame
student_data <- data.frame(StudyHours = study_hours, QuizScores = quiz_scores, ForumPosts = forum_posts, PreviousGrades = previous_grades, FinalGrades = final_grades)

# View the first few rows of the generated data
head(student_data)

  StudyHours QuizScores ForumPosts PreviousGrades FinalGrades
1         20         91         22             78    80.80895
2         12         26         27              1    46.45853
3         13          5          8             60    40.22946
4          4         96         13             78    70.64216
5          5         74         45             31    62.35254
6         18          1         47             50    48.42835

Exploring the data

# Set a fixed random seed for reproducibility
set.seed(10923)

# Number of students
num_students <- 500

# Generate random data for student scores as an example
student_scores <- rnorm(num_students, mean = 75, sd = 10)

# Summary statistics
summary(student_scores)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  46.64   67.81   74.50   74.58   81.00  104.75 

# Histogram of student scores
hist(student_scores, main = "Distribution of Student Scores", xlab = "Scores")

Modeling

Use 80% of the data for training and 20% for testing to predict final grades. Compute the Mean Squared Error and model accuracy based on prediction interval.

# Todo:
# Splitting the data into training and testing sets (80% training, 20% testing)
set.seed(10923) # Set seed for reproducibility
sample_index <- sample(1:nrow(student_data), 0.8 * nrow(student_data))
train_data <- student_data[sample_index, ]
test_data <- student_data[-sample_index, ]

# Building a Linear Regression model using the train data and assign it to an object # called model.
# Todo: Target variable is FinalGrades and the Features are StudyHours, QuizScores, # ForumPosts, and PreviousGrades
# Enter code below:

# Build the linear regression model
model <- lm(FinalGrades ~ StudyHours + QuizScores + ForumPosts + PreviousGrades, data = student_data)

model summary

summary(model)

Call:
lm(formula = FinalGrades ~ StudyHours + QuizScores + ForumPosts + 
    PreviousGrades, data = student_data)

Residuals:
     Min       1Q   Median       3Q      Max 
-13.3924  -3.4734   0.3027   3.0976  16.7901 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)    25.076304   0.762633   32.88  < 2e-16 ***
StudyHours      0.298397   0.037113    8.04 6.66e-15 ***
QuizScores      0.404363   0.007692   52.57  < 2e-16 ***
ForumPosts      0.202482   0.015217   13.31  < 2e-16 ***
PreviousGrades  0.090967   0.007480   12.16  < 2e-16 ***
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Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 4.93 on 495 degrees of freedom
Multiple R-squared:  0.8696,    Adjusted R-squared:  0.8685 
F-statistic: 825.1 on 4 and 495 DF,  p-value: < 2.2e-16

# Making predictions on the test set using the model object
test_predictions <- predict(model, newdata = test_data)

# Evaluation metrics
# Compute the mean squared error (MSE) and R-squared
mse <- mean((test_predictions - test_data$FinalGrades)^2)
rsquared <- 1 - (sum((test_data$FinalGrades - test_predictions)^2) / sum((test_data$FinalGrades - mean(test_data$FinalGrades))^2))

# Print evaluation metrics
cat("Mean Squared Error (MSE): ", mse, "\n")

Mean Squared Error (MSE):  21.81982 

cat("R-squared (R^2): ", rsquared, "\n")

R-squared (R^2):  0.8880908 

Model Accuracy based on Prediction Interval

# Get the predictions and prediction intervals
pred_int <- predict(model, newdata = test_data, interval = "prediction")

# Extract lower and upper bounds of the prediction interval
lower_bound <- pred_int[, "lwr"]
upper_bound <- pred_int[, "upr"]

# Actual values from the test data
actual_values <- test_data$FinalGrades

# Check if the actual values fall within the prediction interval
correct_predictions <- actual_values >= lower_bound & actual_values <= upper_bound

# Compute accuracy
accuracy <- sum(correct_predictions) / length(correct_predictions)

# Print accuracy
cat("Model Accuracy using Prediction Interval:", accuracy, "\n")

Model Accuracy using Prediction Interval: 0.96