Mathematically, a linear regression is defined by this equation:

y = bx + a + ε

Where:

- x is an independent variable.

- y is a dependent variable.

- a is the Y-intercept, which is the expected mean value of y when all x variables are equal

to 0. On a regression graph, it's the point where the line crosses the Y axis.

- b is the slope of a regression line, which is the rate of change for y as x changes.

- ε is the random error term, which is the difference between the actual value of a

dependent variable and its predicted value.

The linear regression equation always has an error term because, in real life, predictors are never

perfectly precise. However, some programs, including Excel, do the error term calculation

behind the scenes. So, in Excel, you do linear regression using the least squares method and

seek coefficients a and b such that:

y = bx + a

For our example, the linear regression equation takes the following shape:

Umbrellas sold = b * rainfall + a

There exist a handful of different ways to find a and b. The three main methods to perform linear

regression analysis in Excel are:

- Regression tool included with Analysis ToolPak

- Scatter chart with a trendline

-Linear regression formula

Below you will find the detailed instructions on using each method.

1- Types of data and level of measurement
2- Graphs and Tables that Represent Categorical Variables
3- Excel formulas
4- Graphs and tables that represent numerical variables
5- Graphs and Tables for Relationships Between Variables.
6- Mean, Median, Mode
7- Variance and Standard Deviation
8- Covariance and Correlation
9- Distributions
10- The Central Limit Theorem
11- Estimators and Estimates
12- Confidence Intervals and the Margin of Error
13- Student’s T Distribution
14- Formulas for Confidence Intervals
15- Scientific method
16- Hypotheses
17- Decisions You Can Take
18- Statistical Errors (Type I Error and Type II Error)
19- P-Value
20- Formulae for Hypothesis Testing
21- Basics
22- Linear regression equation
23- How to do linear regression in Excel with Analysis ToolPak
24- Interpret regression analysis output
25- How to make a linear regression graph in Excel
26- How to do regression in Excel using formulas