Simple Linear Regression Workshop in R

1️⃣ Create a small dataset

We start with study hours and exam scores.

# Sample data
hours  <- c(1,2,3,4,5,6,7,8,9)
scores <- c(35,40,50,55,60,65,70,78,85)

df <- data.frame(Hours = hours, Score = scores)

# Show first rows
head(df)

##   Hours Score
## 1     1    35
## 2     2    40
## 3     3    50
## 4     4    55
## 5     5    60
## 6     6    65

---

2️⃣ Visualize the data

Plot hours vs. score to see if there is a linear trend.

plot(df$Hours, df$Score,
     xlab = "Study Hours",
     ylab = "Score",
     main = "Hours vs Score",
     pch = 19, col = "blue")

---

3️⃣ Fit a linear regression model

Use lm() to estimate the relationship.

model <- lm(Score ~ Hours, data = df)  # fit model
summary(model)                          # see coefficients & R²

## 
## Call:
## lm(formula = Score ~ Hours, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.91111 -0.84444  0.02222  0.95556  2.35556 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  29.4444     1.0737   27.43 2.20e-08 ***
## Hours         6.0667     0.1908   31.80 7.87e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.478 on 7 degrees of freedom
## Multiple R-squared:  0.9931, Adjusted R-squared:  0.9921 
## F-statistic:  1011 on 1 and 7 DF,  p-value: 7.866e-09

---

4️⃣ Add regression line to plot

plot(df$Hours, df$Score,
     xlab = "Study Hours",
     ylab = "Score",
     pch = 19, col = "blue")
abline(model, col = "red", lwd = 2)     # draw line of best fit

---

5️⃣ Predictions and evaluation

Compute predicted scores, Mean Squared Error, and R².

df$Predicted <- predict(model, newdata = df)

# Mean Squared Error
mse <- mean((df$Score - df$Predicted)^2)
cat("Mean Squared Error:", mse, "\n")

## Mean Squared Error: 1.698765

# R-squared (goodness of fit)
summary(model)$r.squared

## [1] 0.9931241

---

6️⃣ Predict for new study hours

Example: what score for 7.5 study hours?

new_hours <- data.frame(Hours = 7.5)
predict(model, new_hours)

##        1 
## 74.94444

---

7️⃣ (Optional) Nice plot with ggplot2

library(ggplot2)

ggplot(df, aes(x = Hours, y = Score)) +
  geom_point(color = "blue", size = 3) +
  geom_smooth(method = "lm", se = FALSE, color = "red") +
  labs(title = "Study Hours vs Score",
       x = "Hours", y = "Score")

## `geom_smooth()` using formula = 'y ~ x'

---