Linear regression estimates how much variable Y changes with every unit of change in X. The general linear regression equation is represented as follows: Y = a + bX Where, X is the independent explanatory variable and Y is the dependent variable. The line has a slope b, and a is the intercept, that is […]

# Linear Regression

## Standard Error of Estimate (SEE)

A linear regression gives us a best-fit line for a scatterplot of data. The standard error of estimate (SEE) is one of the metrics that tells us about the fit of the line to the data. The SEE is the standard deviation of the errors (or residuals). This video by Bionic turtle explains the concept […]

## Coefficient of Determination (R-Squared)

The coefficient of determination measures the percentage of variation in Y that is explained by the model and will be between 0 and 1. To explain the R-squared (coefficient of determination), in this video the author compares it to the standard error of estimate (a measure of the line’s accuracy) and the correlation (the square […]

## Sample Regression Function (SRF)

This video introduces the idea of statistical inference as a way to understand the sample regression function. Statistical inference gives us the ability to draw a sample and based on that sample make an inference about larger population that we don’t have access to. Each sample has a sample regression function (SRF). This video is […]

## Ordinary Least Squares (OLS)

Ordinary Least Squares (OLS) minimizes the residual sum of squares (RSS). RSS is the sum of each squared residual (residual = the observed Y minus the predicted “on the line” Y). Also, about the OLS: the average residual is always zero, and the line passes through the point (average X, average Y). This video by […]

## Standard Error in Linear Regression

A simple (two-variable) regression has three standard errors: one for each coefficient (slope, intercept) and one for the predicted Y (standard error of regression). While the population regression function (PRF) is singular, sample regression functions (SRF) are plural. Each sample produces a different SRF. So, the coefficients exhibit dispersion (sampling distribution). The standard error is […]

## ANOVA Table in Regression

This video explains the Analysis of Variance (ANOVA) table in a two variable regression. The ANOVA table explains the sources of variation. Analysis of Variance (ANOVA) consists of calculations that provide information about levels of variability within a regression model and form a basis for tests of significance.

## Using LINEST() Function in Excel for Multivariate Regression

The LINEST() function calculates the statistics for a line by using the “least squares” method to calculate a straight line that best fits your data, and returns an array that describes the line. Because this function returns an array of values, it must be entered as an array formula. The equation for the line is […]