Linear regression estimates how much variable Y changes with every unit of change in X. The general linear regression equation is represented as follows:

<b>Y = a + bX</b>

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 the value of y when x=0.

The following video by Bionic Turtle explains the concept of linear regression in detail.

<iframe width="600" height="338" src="http://www.youtube.com/embed/ocGEhiLwDVc?list=EC9DFEA77BEEB2535F&amp;hl=en_US" frameborder="0" allowfullscreen></iframe>

Introduction to Linear Regression

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 of Standard Error of Estimate (SEE) in detail and illustrates how it is calculated.

<iframe width="600" height="450" src="http://www.youtube.com/embed/dJR1WqeBgCg" frameborder="0" allowfullscreen></iframe>

Standard Error of Estimate (SEE)

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 <a href="https://financetrain.com/standard-error-of-estimate-see/" title="Standard Error of Estimate (SEE)">standard error of estimate</a> (a measure of the line's accuracy) and the correlation (the square root of the coefficient of determination). All three are measures of the line's fit to the data.

<iframe width="600" height="450" src="http://www.youtube.com/embed/unil0JmtU0g" frameborder="0" allowfullscreen></iframe>

Coefficient of Determination (R-Squared)

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).

<iframe width="600" height="338" src="http://www.youtube.com/embed/qPga0OBV-O8?list=EC9DFEA77BEEB2535F&amp;hl=en_GB" frameborder="0" allowfullscreen></iframe>

<em>This video is developed by David from Bionic Turtle.</em>

Sample Regression Function (SRF)

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 Bionic Turtle explains this method of ordinary least squares (OLS).

<iframe width="600" height="338" src="http://www.youtube.com/embed/MwokVxy5tvg?list=EC9DFEA77BEEB2535F&amp;hl=en_GB" frameborder="0" allowfullscreen></iframe>

Ordinary Least Squares (OLS)

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 <a href="https://financetrain.com/standard-error-of-estimate-see/" title="Standard Error of Estimate (SEE)">standard error</a> is the measure of this dispersion: it is the standard deviation of the coefficient.

In this video, David from Bionic Turtle talks about the standard error in linear regression.

<iframe width="600" height="338" src="http://www.youtube.com/embed/_Rm8W-c6Xko?list=EC9DFEA77BEEB2535F&amp;hl=en_US" frameborder="0" allowfullscreen></iframe>

Standard Error in Linear 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.

<iframe width="600" height="338" src="http://www.youtube.com/embed/8R6UcK91Cec?list=EC9DFEA77BEEB2535F&amp;hl=en_US" frameborder="0" allowfullscreen></iframe>

ANOVA Table in 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 y = mx + b or y = m1x1 + m2x2 + ... + b (if there are multiple ranges of x values) where the dependent y value is a function of the independent x values.

The LINEST() function returns an array, so you need to start by selecting a range and finish with CTRL+SHIFT+ENTER.

The following is a step by step tutorial of analyzing data and running a simple multivariate regression in Excel using LINEST.

<iframe width="600" height="338" src="http://www.youtube.com/embed/s2vOA8D4acQ" frameborder="0" allowfullscreen></iframe>

Using LINEST() Function in Excel for Multivariate Regression

Linear Regression

This frontmatter description will appear below the title

COURSE

Linear Regression

Lessons

R Programming Bundle: 25% OFF