Effect of independent study hours and attendance on high school mathematics exam scores

Project info

• Field of studyEducation and Learning
• LevelUndergraduate thesis (S1)
• Method typeRegression
• Estimated build time± 3 working days
• Toolsstats::lm, lmtest::bptest, lmtest::dwtest, car::vif, ggplot2
• PriceUS$16 - US$106

Research goal

Testing the effect of weekly independent study and attendance rate on mathematics exam score while checking the classical regression assumptions (the analysis is illustrated with synthetic data).

Variables

Example result

• 0.831R2
• 0.829Adjusted R2
• <0.001F-test p-value
• 1.113Coef. Independent
• 0.02Shapiro-Wilk p
• 0.016Breusch-Pagan p

The model explains 83.1% of the variance in Mathematics exam score (R2 = 0.831, F-test p < 0.001). A one-unit increase in Weekly independent study changes Mathematics exam score by 1.113 (p < 0.001). Shapiro-Wilk (p = 0.020) and Breusch-Pagan (p = 0.016) flag an assumption worth checking; maximum VIF is 1.01.

Computed from illustrative synthetic data, not from a real study.

About Multiple Linear Regression with Classical Assumption Tests

Multiple linear regression models the effect of several predictors on one numeric response using ordinary least squares (OLS), together with the classical assumption tests. It is the most common method in undergraduate and master's theses for testing partial (t-test) and joint (F-test) effects.

Steps

1. 1Prepare the data and define the response and predictors
2. 2Fit the model with lm() and read summary(): coefficients, t-tests, F-test, R2
3. 3Test residual normality with Shapiro-Wilk and a Q-Q plot
4. 4Test for heteroscedasticity with Breusch-Pagan (lmtest::bptest)
5. 5Test autocorrelation with Durbin-Watson and multicollinearity with VIF (car::vif)
6. 6Interpret the coefficients and adjusted R2, and plot residual diagnostics

Assumptions to check

• The predictors relate linearly to the response
• Residuals are normal with constant variance (homoscedastic)
• Residuals are not autocorrelated
• Predictors are not highly collinear (VIF < 10)

Reading and reporting the results

Report the regression equation, the sign and size of each coefficient with its t-test p-value, the F-test and adjusted R2. Include the classical assumption tests; if one fails, consider a transformation or robust standard errors.

Example R code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

# Contoh kode R: Multiple Linear Regression with Classical Assumption Tests
suppressPackageStartupMessages({
  library(ggplot2)
  library(patchwork)
  library(lmtest)
  library(car)
})
set.seed(42)
# ---- Gaya grafik ----
pal <- c("#1f6feb", "#e8590c", "#2f9e44", "#ae3ec9", "#f59f00")
warna <- list(bg = "#f4f6fa", panel = "#ffffff", teks = "#1f2933", redup = "#5f6b78", grid = "#e3e8ee", bar = "#1d3557")
tata <- 1
theme_set(theme_minimal(base_size = 11) + theme(legend.position = "bottom"))

# ---- Data sintetis ----
n <- 200
d <- data.frame(weekly_independent_study = rnorm(n, 50, 10),
                attendance_rate = rnorm(n, 30, 6))
z1 <- as.numeric(scale(d$weekly_independent_study))
z2 <- as.numeric(scale(d$attendance_rate))
b1 <- runif(1, 0.45, 0.85)
b2 <- runif(1, 0.15, 0.5) * sample(c(-1, 1), 1)
d$mathematics_exam_score <- 100 + 15 * (b1 * z1 + b2 * z2 + rnorm(n, 0, runif(1, 0.45, 0.8)))
write.csv(d, "data_contoh.csv", row.names = FALSE)

# ---- Analisis: regresi linear berganda (OLS) ----
fit <- lm(mathematics_exam_score ~ weekly_independent_study + attendance_rate, data = d)
s <- summary(fit)
print(s)

# ---- Uji asumsi klasik ----
sw <- shapiro.test(residuals(fit))   # normalitas residual
bp <- lmtest::bptest(fit)            # heteroskedastisitas (Breusch-Pagan)
dw <- lmtest::dwtest(fit)            # autokorelasi (Durbin-Watson)
vf <- car::vif(fit)                  # multikolinearitas
print(sw); print(bp); print(dw); print(vf)


# ---- Grafik ----
d$prediksi <- fitted(fit)
d$residual <- residuals(fit)
p1 <- ggplot(d, aes(weekly_independent_study, mathematics_exam_score)) +
  geom_point(colour = pal[1], alpha = 0.55, size = 1.8) +
  geom_smooth(method = "lm", formula = y ~ x, colour = pal[2], fill = pal[2], alpha = 0.18, linewidth = 1.1) +
  labs(title = "Partial relationship with OLS fit", x = "weekly_independent_study", y = "mathematics_exam_score")
p2 <- ggplot(d, aes(prediksi, residual)) +
  geom_hline(yintercept = 0, linetype = "dashed", colour = warna$redup) +
  geom_point(colour = pal[3], alpha = 0.6, size = 1.5) +
  geom_smooth(method = "loess", formula = y ~ x, se = FALSE, colour = pal[2], linewidth = 0.8) +
  labs(title = "Residuals vs fitted", x = "Fitted value", y = "Residual")
p3 <- ggplot(d, aes(sample = residual)) +
  stat_qq(colour = pal[1], alpha = 0.6, size = 1.3) +
  stat_qq_line(colour = pal[2], linewidth = 0.9) +
  labs(title = "Normal Q-Q of residuals", x = "Theoretical quantile", y = "Sample quantile")
p_hasil <- if (tata == 1) p1 | (p2 / p3) else p1 / (p2 | p3)

print(p_hasil)

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• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

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