Line of Best Fit

A line of best fit is a straight line that best represents the data on a scatter plot, showing the trend of the data points.

Correlation measures the strength and direction of a linear relationship between two quantitative variables.

The equation of a line in slope-intercept form is given by $$y = mx + b$$ , where $$m$$ is the slope and $$b$$ is the y-intercept.

A positive correlation indicates that as one variable increases, the other variable also tends to increase.

A negative correlation indicates that as one variable increases, the other variable tends to decrease.

The slope of a line of best fit can be determined by calculating the change in y over the change in x (rise over run) between two points on the line.

A scatter plot is used to visually display the relationship between two quantitative variables, helping to identify trends, patterns, or correlations.

The y-intercept is the value of y when x is zero, indicating the starting point of the line on the y-axis.

The correlation coefficient (r) is calculated using the formula: $$r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}$$ .

If the correlation coefficient is close to 1, it indicates a strong positive linear relationship between the two variables.