Least squares regression

Definition

Least squares regression is a statistical method used to determine the best-fitting line through a set of data points by minimizing the sum of the squares of the vertical distances between the data points and the line. It is commonly used for predictive modeling and trend analysis.

5 Must Know Facts For Your Next Test

1. The least squares regression line is also known as the line of best fit.
2. The formula for the least squares regression line is $y = mx + b$, where $m$ represents the slope and $b$ represents the y-intercept.
3. To calculate $m$ (slope), use $$m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}$$.
4. To calculate $b$ (y-intercept), use $$b = \frac{(\sum y)(\sum x^2) - (\sum x)(\sum xy)}{n(\sum x^2) - (\sum x)^2}$$.
5. The coefficient of determination ($R^2$) measures how well the regression line approximates real data points; an $R^2$ value closer to 1 indicates a better fit.

Review Questions

• What is the purpose of using least squares regression in data analysis?
• How do you interpret the slope ($m$) and y-intercept ($b$) in a least squares regression equation?
• What does an $R^2$ value close to 1 signify in terms of model fit?

Related terms

Correlation Coefficient: A measure that determines the degree to which two variables' movements are associated. It ranges from -1 to +1.

$R^2$ Value: Also known as the coefficient of determination, it indicates how well data points fit a statistical model – typically a linear regression model.

Residuals: The differences between observed values and predicted values in a regression analysis, representing error terms.