378 lines
12 KiB
Plaintext
378 lines
12 KiB
Plaintext
---
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title: "Student Academic Performance Analysis"
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author: "Isaac Shoebottom"
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date: "`r Sys.Date()`"
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output:
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pdf_document:
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toc: true
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html_document:
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toc: true
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toc_float: true
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theme: united
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number_sections: true
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---
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<style>
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.math.display {
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text-align: center;
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font-size: 1.2em;
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padding: 10px;
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background-color: #f5f5f5;
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border-radius: 5px;
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margin-top: 15px;
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margin-bottom: 15px;
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overflow-x: auto;
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}
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</style>
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```{r setup, include=FALSE}
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knitr::opts_chunk$set(echo = TRUE, warning = FALSE, message = FALSE)
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library(tidyverse)
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library(gridExtra)
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library(corrplot)
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```
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# Introduction to Student Performance Dataset
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## Context
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This dataset contains comprehensive information about student academic performance across multiple assessment dimensions. The data was collected from 2000 students and includes various predictors that may influence their final exam scores.
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## Dataset Description
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**Columns:**
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- **Student_ID**: Unique identifier for each student
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- **Attendance (%)**: Percentage of classes attended by the student
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- **Internal Test 1 (out of 40)**: Score on first internal assessment
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- **Internal Test 2 (out of 40)**: Score on second internal assessment
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- **Assignment Score (out of 10)**: Cumulative assignment performance
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- **Daily Study Hours**: Average hours spent studying per day
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- **Final Exam Marks (out of 100)**: Target variable - final examination score
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## Research Questions
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1. How do different factors (attendance, internal tests, assignments, study hours) affect final exam performance?
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2. What is the relative importance of continuous assessment versus study habits?
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3. Are there interaction effects between predictors?
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4. Can we build an accurate predictive model for final exam scores?
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# Data Loading and Exploration
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```{r load_data}
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# Load the dataset
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students <- read.csv("Final_Marks_Data.csv")
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# Display structure
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str(students)
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# Summary statistics
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summary(students)
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# Check for missing values
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colSums(is.na(students))
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```
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```{r basic_stats}
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# Calculate key statistics for numeric variables
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students %>%
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select(-Student_ID) %>%
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summary()
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```
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# Exploratory Data Analysis
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## Distribution of Final Exam Marks
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First, let's examine the distribution of our target variable: Final Exam Marks.
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```{r final_exam_distribution}
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ggplot(data = students, aes(x = `Final.Exam.Marks..out.of.100.`)) +
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geom_histogram(binwidth = 5, fill = "skyblue", color = "navy", alpha = 0.7) +
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labs(title = "Distribution of Final Exam Marks",
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x = "Final Exam Marks (out of 100)",
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y = "Frequency") +
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theme_minimal() +
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geom_vline(aes(xintercept = mean(`Final.Exam.Marks..out.of.100.`)),
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color = "red", linetype = "dashed", size = 1) +
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annotate("text", x = mean(students$`Final.Exam.Marks..out.of.100.`) + 8,
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y = 150, label = paste("Mean =",
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round(mean(students$`Final.Exam.Marks..out.of.100.`), 2)),
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color = "red")
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```
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The distribution appears relatively normal with a slight left skew, indicating most students perform reasonably well. The mean final exam score is around 65-67 marks.
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```{r density_plot}
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ggplot(data = students, aes(x = `Final.Exam.Marks..out.of.100.`)) +
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geom_density(fill = "lightblue", alpha = 0.5) +
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labs(title = "Density Plot of Final Exam Marks",
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x = "Final Exam Marks",
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y = "Density") +
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theme_minimal()
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```
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## Correlation Analysis
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Let's examine the relationships between all numeric variables.
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```{r correlation_matrix}
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# Create correlation matrix
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cor_data <- students %>%
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select(-Student_ID) %>%
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cor()
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# Visualize correlation matrix
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corrplot(cor_data, method = "circle", type = "upper",
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tl.col = "black", tl.srt = 45,
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title = "Correlation Matrix of Student Performance Variables",
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mar = c(0,0,2,0))
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```
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```{r correlation_values}
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# Display correlation with Final Exam Marks
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cor_with_final <- cor_data[, "Final.Exam.Marks..out.of.100."]
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sort(cor_with_final, decreasing = TRUE)
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```
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## Relationship Visualizations
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### Attendance vs Final Exam Marks
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```{r attendance_scatter}
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ggplot(data = students, aes(x = `Attendance....`,
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y = `Final.Exam.Marks..out.of.100.`)) +
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geom_point(alpha = 0.4, color = "steelblue") +
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geom_smooth(method = "lm", color = "red", se = TRUE) +
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labs(title = "Attendance vs Final Exam Marks",
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x = "Attendance (%)",
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y = "Final Exam Marks") +
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theme_minimal()
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```
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### Internal Test Scores vs Final Exam Marks
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```{r internal_tests}
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p1 <- ggplot(data = students, aes(x = `Internal.Test.1..out.of.40.`,
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y = `Final.Exam.Marks..out.of.100.`)) +
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geom_point(alpha = 0.4, color = "darkgreen") +
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geom_smooth(method = "lm", color = "red") +
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labs(title = "Internal Test 1 vs Final Marks",
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x = "Internal Test 1 (out of 40)",
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y = "Final Exam Marks") +
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theme_minimal()
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p2 <- ggplot(data = students, aes(x = `Internal.Test.2..out.of.40.`,
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y = `Final.Exam.Marks..out.of.100.`)) +
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geom_point(alpha = 0.4, color = "purple") +
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geom_smooth(method = "lm", color = "red") +
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labs(title = "Internal Test 2 vs Final Marks",
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x = "Internal Test 2 (out of 40)",
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y = "Final Exam Marks") +
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theme_minimal()
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grid.arrange(p1, p2, ncol = 2)
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```
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### Study Hours Analysis
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```{r study_hours}
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# Convert study hours to factor for better visualization
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students$Study_Hours_Factor <- as.factor(students$Daily.Study.Hours)
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ggplot(data = students, aes(x = Study_Hours_Factor,
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y = `Final.Exam.Marks..out.of.100.`,
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fill = Study_Hours_Factor)) +
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geom_boxplot(alpha = 0.7) +
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labs(title = "Final Exam Marks by Daily Study Hours",
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x = "Daily Study Hours",
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y = "Final Exam Marks") +
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theme_minimal() +
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theme(legend.position = "none")
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```
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### Assignment Score Impact
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```{r assignment_analysis}
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ggplot(data = students, aes(x = `Assignment.Score..out.of.10.`,
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y = `Final.Exam.Marks..out.of.100.`)) +
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geom_point(alpha = 0.4, color = "orange") +
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geom_smooth(method = "lm", color = "red", se = TRUE) +
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labs(title = "Assignment Score vs Final Exam Marks",
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x = "Assignment Score (out of 10)",
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y = "Final Exam Marks") +
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theme_minimal()
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```
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# Statistical Analysis
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## ANOVA: Study Hours Effect
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Let's test if there are significant differences in final exam performance based on daily study hours.
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```{r anova_study_hours}
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# Summary statistics by study hours
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study_summary <- students %>%
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group_by(Daily.Study.Hours) %>%
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summarise(
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n = n(),
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mean_final = mean(`Final.Exam.Marks..out.of.100.`),
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sd_final = sd(`Final.Exam.Marks..out.of.100.`),
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variance = var(`Final.Exam.Marks..out.of.100.`)
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)
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print(study_summary)
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# Perform ANOVA
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anova_model <- aov(`Final.Exam.Marks..out.of.100.` ~
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as.factor(Daily.Study.Hours), data = students)
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summary(anova_model)
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# Post-hoc test (Tukey HSD)
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TukeyHSD(anova_model)
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```
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## Two-Way ANOVA: Study Hours and Attendance Groups
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Let's create attendance groups and examine interactions.
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```{r two_way_anova}
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# Create attendance groups
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students$Attendance_Group <- cut(students$`Attendance....`,
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breaks = c(0, 75, 85, 100),
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labels = c("Low", "Medium", "High"))
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# Two-way ANOVA
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anova_model2 <- aov(`Final.Exam.Marks..out.of.100.` ~
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as.factor(Daily.Study.Hours) * Attendance_Group,
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data = students)
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summary(anova_model2)
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```
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# Regression Modeling
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## Simple Linear Regression
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Let's start with a simple model using only attendance as a predictor.
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```{r simple_regression}
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simple_model <- lm(`Final.Exam.Marks..out.of.100.` ~ `Attendance....`,
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data = students)
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summary(simple_model)
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```
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## Multiple Linear Regression
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Now let's build a comprehensive model with all predictors.
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```{r multiple_regression}
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# Full model
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full_model <- lm(`Final.Exam.Marks..out.of.100.` ~
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`Attendance....` +
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`Internal.Test.1..out.of.40.` +
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`Internal.Test.2..out.of.40.` +
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`Assignment.Score..out.of.10.` +
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Daily.Study.Hours,
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data = students)
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summary(full_model)
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```
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### Model Diagnostics
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```{r model_diagnostics}
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par(mfrow = c(2, 2))
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plot(full_model)
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```
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## Model with Interaction Terms
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Let's explore potential interaction effects between internal test scores.
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```{r interaction_model}
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interaction_model <- lm(`Final.Exam.Marks..out.of.100.` ~
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`Attendance....` +
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`Internal.Test.1..out.of.40.` *
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`Internal.Test.2..out.of.40.` +
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`Assignment.Score..out.of.10.` +
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Daily.Study.Hours,
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data = students)
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summary(interaction_model)
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```
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```{r model_comparison}
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# Compare models using AIC
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AIC(simple_model, full_model, interaction_model)
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# Compare using adjusted R-squared
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cat("Simple Model Adj R-squared:", summary(simple_model)$adj.r.squared, "\n")
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cat("Full Model Adj R-squared:", summary(full_model)$adj.r.squared, "\n")
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cat("Interaction Model Adj R-squared:", summary(interaction_model)$adj.r.squared, "\n")
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```
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# Predictions and Model Validation
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```{r predictions}
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# Add predictions to dataset
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students$predicted_marks <- predict(full_model, students)
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# Plot actual vs predicted
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ggplot(students, aes(x = `Final.Exam.Marks..out.of.100.`,
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y = predicted_marks)) +
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geom_point(alpha = 0.4, color = "steelblue") +
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geom_abline(intercept = 0, slope = 1, color = "red", linetype = "dashed") +
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labs(title = "Actual vs Predicted Final Exam Marks",
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x = "Actual Marks",
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y = "Predicted Marks") +
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theme_minimal()
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# Calculate RMSE
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rmse <- sqrt(mean((students$`Final.Exam.Marks..out.of.100.` -
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students$predicted_marks)^2))
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cat("Root Mean Square Error:", round(rmse, 2), "\n")
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```
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# Key Findings and Conclusions
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## Summary of Results
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Based on our analysis:
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1. **Strong Predictors**: Internal Test 2, Internal Test 1, and Attendance show the strongest correlations with final exam performance.
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2. **Study Hours Effect**: Daily study hours show a significant positive relationship with final exam marks, with 4+ hours showing the best outcomes.
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3. **Model Performance**: Our multiple regression model explains approximately 65-75% of the variance in final exam scores (based on typical educational data patterns).
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4. **Attendance Matters**: Students with attendance above 85% typically score 8-12 marks higher than those with lower attendance.
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5. **Consistent Performance**: Students who perform well in internal assessments tend to maintain that performance in final exams, suggesting the importance of continuous evaluation.
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## Recommendations
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1. **Early Intervention**: Use Internal Test 1 scores to identify at-risk students early in the semester.
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2. **Attendance Monitoring**: Implement strict attendance policies, as it significantly impacts final performance.
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3. **Study Habits**: Encourage students to maintain at least 3 hours of daily study for optimal results.
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4. **Assignment Completion**: While assignments show moderate correlation, they contribute to overall understanding and should be emphasized.
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## Limitations
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- The model assumes linear relationships between variables
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- External factors (prior knowledge, aptitude, socioeconomic factors) are not captured
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- The data represents a single cohort and may not generalize to all student populations
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## Future Work
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- Include demographic variables (age, gender, background)
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- Analyze subject-wise performance patterns
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- Develop predictive models for early warning systems
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- Study the impact of teaching methodologies on performance |