• Correlation analysis measures the strength and direction of the linear relationship between two variables.
• It is often used to determine whether a change in one variable is associated with a change in another variable.

• Positive Correlation: As one variable increases, the other variable also increases.
• Negative Correlation: As one variable increases, the other variable decreases.
• No Correlation: There is no linear relationship between the two variables.

• The correlation coefficient \(r\) ranges from -1 to 1.
  • \(r = 1\): Perfect positive correlation.
  • \(r = -1\): Perfect negative correlation.
  • \(r = 0\): No linear correlation.

Suppose we want to analyze the correlation between the height and weight of individuals.

## [1] 0.66713

The correlation coefficient is calculated as follows:

\[ r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}} \]

Where: - \(x_i, y_i\) are the individual sample points. - \(\bar{x}, \bar{y}\) are the means of the respective variables.

Here is the code used to create the scatter plot with a regression line:

p2 <- ggplot(df, aes(x = height, y = weight)) + geom_point(color = “blue”) + geom_smooth(method = “lm”, se = FALSE, color = “red”) + theme_minimal() + labs(title = “Height vs. Weight with Regression Line”, x = “Height (cm)”, y = “Weight (kg)”)

p2 ```

• If \(r > 0\), there is a positive relationship between height and weight.

• If \(r < 0\), there is a negative relationship between height and weight.

• In our example, the correlation coefficient is 0.6671, indicating a positive relationship.

• Correlation analysis helps determine the strength and direction of the relationship between two variables.

• In our example, there is a positive correlation between height and weight.

• This means that as height increases, weight also tends to increase.