Bivariate Data

Bivariate Data

Data that involves two variables being measured for each case, such as height and weight.

Explanatory Variable (EV)

The variable believed to influence the other variable; it is independent.

Response Variable (RV)

The variable that responds to the change in the explanatory variable; it is dependent.

Scatter Plot

A graph plotting pairs of values where the x-axis represents the explanatory variable and the y-axis represents the response variable.

Pearson’s Correlation Coefficient (r)

A statistic that measures the strength and direction of a linear relationship between two variables, ranging from -1 to 1.

Strong Correlation

When the absolute value of r is close to 1, indicating a strong linear relationship.

Weak Correlation

When the absolute value of r is close to 0, indicating a weak linear relationship.

Least Squares Regression Line (LSRL)

The best-fit line that minimizes the squared vertical distances from data points to the line used to predict values.

Slope (b)

Indicates how much the response variable changes for each 1 unit increase in the explanatory variable.

Intercept (a)

The predicted value of the response variable when the explanatory variable is 0.

Coefficient of Determination (r²)

The percentage of variation in the response variable explained by the explanatory variable.

How to construct a scatter plot?

Plot each pair of values using the explanatory variable on the x-axis and the response variable on the y-axis.

What does r² = 0.85 indicate?

85% of the variation in the response variable is explained by the explanatory variable.

How to make predictions using the LSRL?

Substitute an x-value into the regression equation to calculate the corresponding y-value.