# Bivariate Statistics

# Overview of Bivariate Statistics

**Bivariate statistics**analyses the relationship between two variables. It is an essential part of statistical methodology.- This method determines the
**degree of correlation**between the two variables, the**direction**of this correlation, and its**graphical representation**.

# Key Concepts

**Scatterplot**: A graphical representation of the degree and direction of correlation between two variables.**Line of Best Fit/Regresion Line**: A line which depicts the trend observed in the scatterplot.**Correlation coefficient**: A numerical value typically ranging from -1 to 1 representing the degree of correlation between two variables.*(r) or (rho)*

# Drawing Scatter Plots and Lines of Best Fit

- A scatterplot is prepared with the independent variable on the horizontal axis and the dependent variable on the vertical axis.
- Each data point is represented by a dot on the scatterplot.
- The
**line of best fit**is drawn in such a way that it minimizes the distance between the line and all the plotted points.

# Calculating the Correlation Coefficient

**Positive correlation**: As one variable increases, so does the other resulting in a correlation coefficient between 0 and 1.**Negative correlation**: As one variable increases, the other decreases resulting in a correlation coefficient between 0 and -1.- A correlation coefficient near to 0 suggests a weak or non-existent relationship between variables.

# Interpreting the Correlation Coefficient

- A positive correlation coefficient signifies direct proportionality between variables, while a negative one shows inverse proportionality.
- The closer the absolute value of the correlation coefficient to 1, the stronger the relationship between variables.
- A correlation coefficient of 0 signifies no linear relationship between the variables.

# Types of Correlation

**Perfect positive correlation**: A correlation coefficient of 1 where all points lie on a line sloping upwards.**Perfect negative correlation**: A correlation coefficient of -1 where all points lie on a line sloping downwards.**No correlation**: A correlation coefficient of 0 where points are widely scattered and depict no pattern.

# Data Transformation

**Data transformation**can be used to achieve linearity in the correlation, such as square root transformation, log transformation, etc.- Only apply transformations to data where the correlation is not linear when plotted in its original form.

# Causality

- While bivariate statistics can identify relationships between variables, they do not necessarily demonstrate cause and effect.
- Be wary of the potential for
**confounding variables**to inaccurately suggest a direct relationship between two variables.