# How to do Regression Analysis in Excel

The regression analysis has been a tool used for ages in understanding and determining the nature of different phenomenon utilising a set of data. The tool enables data analysts in forecasting the outcome of an unknown collection of data, hence useful in determining the trends. Therefore, data analysts must learn how to do regression analysis in Excel to identify the trends in phenomena. Lessons on how to do regression analysis have been on

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Regression is a statistical tool used in statistics, finance, and other disciples to determine the relationship between a dependent variable and an independent variable. Regression analysis helps investors and financial managers to assess and understand the relationship between two variables, such as the market prices and the stock present. For this reason, it is essential to master the guidelines on how to do regression analysis in Excel.

## Types of Regression

The different kinds of regression include:

• Linear regression
• Logistic regression
• Polynomial regression
• Stepwise regression
• Ridge regression
• Lasso regression
• Elastic Net regression

Data analysts categorise the types of regression based on the following factors:

1. The number of independent variables
2. The shape of the regression curve or line
3. The nature of the dependent variable

For this article, we shall focus on linear regression to demonstrate how to do regression in excel.

### Understanding Linear Regression

Linear regression is a commonly used modeling technique for data analysis. This type of regression technique is among the first few techniques leant by data analysts while learning on predictive models.

In linear regression, the dependent variable is continuous, whereas the independent variable(s) is either discrete or continuous. The nature of the regression line is always linear, giving the technique the name linear regression.

Linear regression determines the correlation between a dependent variable (Y) and either one or more independent variables (X). The determination of the relationship is by using a line of best fit (a regression line).

The two types of linear regression include:

1. Simple linear regression: the analysis uses a single (one) independent variable to predict or explain the nature of a dependent variable(y).
2. Multiple linear regressions: the analysis uses more than one independent variable to predict, determine or understand the nature of dependent variables.

#### The Line of Best Fit

The line of best fit can be obtained by joining closely related points or by using the Least Square Method. The Least Square Method assists in formulating a fitting regression line. By using the method, one can calculate the line of best fit from the available observed data.

The least Square method minimises the sum of the squares of deviations from each data point to the line. Since the deviations are first squared, there is no cancellation of the negative and the positive values.

#### Expressions for Linear Regression

The general expression for linear regression is:

Simple linear regression: Y = a + bX + c

Multiple linear regression: Y= a + b1X1 + b2X2 + b3X3 + … bzXz + c

Where:

Y = the dependent variable (the value you are trying to determine)

X= the independent variable (the value(s) you are using to determine the value(s) of Y).

a= the intercept

b= the gradient (slope)

c= the residual (error)

In general, linear regression uses a group of different variables to predict the outcomes of other variables denoted by Y. regression helps in determining the mathematical relationship between the two. In regression, the assessment of the relationship is by use of a straight line (linear regression) to approximate the values of other data. It is important to note that when analysing data of multiple regressions, you have to differentiate the variables by using superscripts.

#### The Linear Model Assumptions

There are six basics assumptions made when employing the linear regression technique:

1. The variables (the dependent and independent variables) depict a linear correlation between the slope (gradient) and the intercept
2. The independent variable is not random
3. The values of the residual is zero
4. The residual or error values is constants across all observations
5. The value of the error or residual is not correlated across all observations
6. The values of the residual or error usually follows the normal distribution

## The Importance of Using Regression Analysis

The two main benefits of using regression as a statistical tool are:

1. Regression analysis shows the relationship between a dependent variable and an independent variable. The technique is vital in forecasting, the modeling of time series as well as finding the relationship between two or more different variables.
2. Regression analysis indicates the strength of the impacts of several independent variables on a dependent variable

In the field of finance, regression analysis is important in assisting finance professional in predicting sales of a company bases in previous sales, weather, GDP growth and other conditions. This way, these finance professionals can determine their business patterns. Furthermore, the use of regression in Capital Asset Pricing Model (CAPM) assists investment and finance professionals in pricing assets as well as determining the costs of capital.

## Data Analysis Excel

Excel has several essential features designed to perform data analysis. Some of this feature includes Sort, Filters, Conditional Formatting, Charts, Pivot Table, solver, tables, analysis ToolPak.

• Sort: This feature allows sorting of data in excel in the following manner:
1. Ascending or descending manner
2. Single or multiple columns
3. By color
4. Randomised or reverse list

• Filters: this feature can filter excel data in a certain way you want it to appear or meet a certain standard. This filter can be done based on date, advanced filters, number, subtotal, or duplicate.
• Conditional Formatting: This feature highlights data in excel using colours.
• Charts: excel has several maps that can make graphs, bar graphs, and many others.
• Pivot Table: enhances the extraction of essential data from detailed or extensive data.
• Tables: enhance more available data analysis in excel. For example, excel has a multi-level, group, and updated pivot tables, e.g., style of tables and structured references.
• What-if analysis: provides an opportunity to use different scenarios for a specific formula.
• The solver: used in getting a solution for various decision issues in research.
• Analysis ToolPak: an add-in program in Excel that carries out data analysis for statistical, financial and engineering fields. The analysis might be through ANOVA, regression, Histogram, correlation and Descriptive statistics

### Regression in Analysis

Regression in excel refers to an analytical technique that assists data analysts in the estimation and prediction of unknown digits of one variable using the values of another known variable.

#### Linear Regression Excel

Analysis ToolPak add-in is an essential tool for linear regression in Excel. With this add-in tool, it becomes easier to learn how to do regression in excel. The steps of the addition of the ToolPak include:

• Open excel> file> click options
• On the left bar of the excel dialogue box, select Add-ins. In the manage Box, confirm whether Excel Add-in is selected, then click Go.
• After opening the Add-in dialogue box, then tick off the analysis of ToolPak then press or select OK.
• This step allows the addition of Data Analysis Tools to the data tab in the excel ribbon.
• Then Run regression analysis to perform a simple linear regression in excel.

Click Data Analysis Button in the analysis button on the Data tab.

Choose regression and then select OK.

Configure the following in the regression dialogue box.

• Choose the Input Y range, which represents the dependent variable.
• Select the input X range, which represents the independent variable.
• Confirm if the X and Y ranges have labels in the Label box.
• Choose a new worksheet or preferred option.
• To get actual and predicted numbers, select the residual checkbox.

Click OK and see the regression results generated by excel.

##### How to Plot Linear Regression

Follow these steps to plotting the linear regression line.

First, from your data, create a scattered plot graph using the basic graphing module.

• Highlight the data that you want to plot.
• From the toolbar, Open the Chart Wizard or click insert
• When the first Chart Wizard pops up, select XY to scatter and the icon with unconnected points.
• By Clicking Next, the data range box will reflect the highlighted values in the spreadsheet.
• By clicking Next, the wizard will display a dialogue box where you will enter the Beer Law for the Title, Absorbance for Y-axis, and Concentration for X-axis.
• Click the legend tab then click off option on the legend tab. The finish to display the scattered plot on the same spreadsheet.
1. Highlight scattered plots.
2. Click Charts then add a trend line to open a dialogue box.
3. Choose Linear or regression type.
4. By clicking the options Tab, the display equation on the chart will appear, then click OK.
5. The display will show a linear regression line.

#### Interpreting Regression Analysis Excel

Running regression in excel is more accessible since excel generates the results automatically. However, interpreting regression excel is slightly difficult since it requires an understanding of what is behind each value.

#### Forecasting Linear Regression in Excel

Forecasting by use of linear regression in Excel is commonly used in business and marketing to predict future prices and market changes.

1. First, develop a scatter plot
2. Plot a line of best fit from the scatter plot
3. The scattered plot can be a history of sales, and the trend line (line of best fit) is the actual linear regression equation that can predict future transactions or forecasted sales or value
4. Generate linear equations from the line of best fit. The general formula of linear equations is Y = a + bX + c.
5. Insert the generated formula in an excel cell
6. Click on the first cell of the forecast (e.g. C58)
7. Insert the generated formula Y = a + bX + c.
8. Insert the values of the known variables in one column
9. Copy the formula down the column to generate the predicted values
10. Prediction values will be generated automatically for forecasting.

#### Multiple Regression Analysis Excel

1. Launch excel to begin multiple regression> click File> the select option.
2. On the left side of the Options dialogue box, click on Add-in tab
3. Click Analysis ToolPak
4. Scroll the Top-down menu and select Excel Add-Ins
5. Click Go to open Add-ins dialogue box.
6. Click in the checkbox in front of the Add-in select OK.
##### How to Do Multiple Regression
1. Click the Data Tab
2. Extensive analysis group then click the Data tab. The dialogue box for data analysis will launch.
3. In the data analysis, dialogue box, click Data Analysis.
4. Select analysis tools, and then click on regression then OK.
5. Type the range of cells in the cell named Input Y range or in the dependent variable cell and also, type location of range in the Input X Range cell or independent variable.
6. Click on ‘Label’ in the checkbox to ensure Excel is aware of the first row had labels only.
7. Open the Output options and click on the Output range.
8. Enter the data range to determine where the regression analysis will show in the first order.
9. Then click on Worksheet Ply. If you want results to display on different worksheets, then click New Workbook.
10. By clicking the Plot checkbox, the results will show on a graph. But clicking residual plot, residuals will be graphed separately. Also, by clicking the Line Fit Plot, the prediction will be graphed against real results.
11. Finally, by clicking OK, regression will start processing and view the results in the selected specified location initially.

##### Multiple Regression Forecasting Excel
1. First, open Microsoft excel
2. Click on the “Data” tab to check whether the “Data Analysis” ToolPak is active
3. Insert your data manually or open your data file. Arrange the data in adjacent columns with the labels in the first row of each column
4. Click on the “Data” tab, then click on “Data Analysis” in the “Analysis grouping.”
5. Input the dependent (Y) data by first placing the cursor in the “Input Y-Range” field, then highlighting the column of data in the workbook.
6. The independent variables are entered by first placing the cursor in the “Input X-Range” field, then highlighting multiple columns in the workbook
7. Select the desired options in the “Residuals” category.  Click “OK”, and the analysis will be created.

#### How to do Non-linear Regression in Excel

1. First, any at any position inside the data chart, right click your mouse
2. A Manu will pop up then click select Trend Manu. Six potential trends Manu that appear in Microsoft Excel include power, polynomial exponential, logarithmic, linear, and moving average.
3. Select the power curve because it looks similar to the Trend.
4. Select the Options Tab, then confirm the R-squared value and display equation
5. Click the OK button to obtain a Non-linear regression graph or plot together with the value for R-squared.

### Least-Squares Regression Excel

Least square regression excel is one of regression analysis methods that display how independent and dependent variables relate along with linear lines or the line of best fit. However, the primary goal of least square regression is making sure a straight line is drawn on a graph passing through common points with the closest relation amongst the values. For example, working on data with two variables that is y and x-axis plotted on a graph using the x values and y values. Draw straight line passing through a common point generates a line of best fit.

The formula ŷ = a + bx where ŷ = dependent variable where x = independent variable, a = y-intercept, b = slope of the line is used to calculate least square regression line. However, this equation can be solved using excel.

#### Follow these steps to perform the linear regression equation in Excel.

1. Start by inserting the data in the data in the excel spreadsheet
2. The data has to variable the independent and dependent variables represented by y and x values.
3. Then, highlight the data and insert a scatter graph by use of data points.
4. Then input a trend line in the scatter graph.
5. Select the trend line option and then choose the trend line and then select the display equation from the chart.
6. The least-square equation is generated depending on the data inserted in the excel spreadsheet.
7. Then calculation can do for the generated least of square regression

This method of regression analysis is the most suitable technique for the prediction of analysis and model. It is used frequently in the field of marketing, finance, and economics because future variables and the current values relationships are essential. Moreover, this method is simple and easy to compute, and it provides the closest link between dependent, independent, and predictive variables.

### Regression Analysis Excel Mac

1. First, run the Excel for Mac 2016 on your computer.
2. On the Tools Manu at the top of the Excel, Select Add-ins
3. Tick each box of Solver Add-ins and Analysis ToolPak. These tools are essential for the analysis of engineering and Statistical data.
4. After ticking the two boxes, select the tab for data.
5. Then, choose either Data Analysis or solver depending on your data or the purpose of data analysis.
6. After opening the Data analysis, a dialogue box will open and then select Correlations.
7. Highlight the entire data, including the names of the columns.
8. Right-click, then in the delete the output range and insert desired range depending on your data
9. Then press, OK.
10. To round off the values, go to the numbers in the top menu and press on Numbers.
11. To predict the unknown value, graph a scatter plot. The equation generated from the trendline is called a regression equation, which predicts the known values.
12. To generate a scatter plot, go to the top menu, then press scatter chart.
13. Click on the first chart to generate a scatter plot automatically, showing the dependent and independent variables.
14. Then, customise the chart.
15. Open format trendline, the select Linear
16. Select equation display and R-square button to insert in the linear trendline.
17. The read the test score on the y-axis and predict the unknown values on the x-axis.

### How to Find R2 Value in Excel

Excel uses the RSQ function to get the R-squared value of a set of data.

=RSQ (known Ys, known Xs)

Where:

Known Ys = the dependent variables

Known Xs = the independent variables

Note: The value of Xs and those of Ys should be the same in number. If one column has, say six values and the other 4 or 5, there will be an error.

1. Enter your known Ys in range A2: A9 and the known Xs in range B2: B9
2. Enter the RSQ function in the Cell A12. i.e. =RSQ (B2:B9, A2:A9)
3. Hit enter to produce the R2 value

#### How to Interpret R-Squared

The r- squared value always falls between 0.0- 1.0. When multiplied by 100, then the value should be between 0%- 100%. A 0% r-squared valued means that there is no probability of falling data point on the regression line.

In case the value is 100%, then the probability of falling data point of the regression line is 100%.

### Multiple Regression Scatter Plot Excel

Multiple regression refers to add on or extent of simple linear regression information which predicts the unknown variables basing on the two or more values. How you can plot these values using excel for graphical representation. First, these steps generate a Scatter graph called the XY graph. It can also refer to a two-dimensional diagram that indicates the relationship between two variables.

Vertical and horizontal axes in a scatter plot of multiple regression are values axes that plot numerical data. The dependent variable is a plot on the vertical axes and the dependent variable on the vertical axis.

#### Arrangement of Data for Scatter Chart

A scatter graph has two qualitative variables that are interrelated. Therefore, you require two sets of numerical data in two distinct columns. Enter the Independent variable in the left columns and insert the dependent variable in the right column. The plotting of the dependent variable should be on the x-axis because it influences the dependent variable on the y-axis.

#### How to Develop Multiple Regression Scatter Plot Excel

The essential steps involved in the creation of the scatter plot in excel are as follows.

1. First, start by selecting the entire data in the excel spreadsheet. Involve the column headers always during selection or highlighting. Remember, do not involve any other column to prevent any confusion
2. Click the Insert tab.
3. Select chart groups.
4. Next, click on the icon of scatter charts.
5. Choose the template of your interest.
6. Click on the first thumbnail to enhance the insertion of the classic scatter graph. This step `will generate the scatter plots automatically.

#### Types of Multiple Regression Scatter Plot Excel

• The scatter plot chart that has a smooth line.
• The scatter plot chart with a straight line.
• The scatter plot chart which contains straight lines with the marker
• The scatter plot chart that has smooth range and makers

#### How to customise a Multiple Regression Scatter Plot Excel

You can customise all types of multiple scatter plots on excel by changing the axis gridlines, the colour of charts, and the chart title. Follow these steps to modify Scatter Plots in excel.

1. Place the mouse on the x-axis then right-click.
2. Select format axis
3. Select the interested maximum and minimum bounds appropriately on format axis
4. This step can also allow you to make changes in significant units in between the gridlines.

### How to Do Labelling Of Multiple Scatter Plot Charts

Labelling scatter charts provide a clears vision of the chart and easily understandable. Use the following steps are to do the labelling.

1. Start by selecting the plot.
2. Then click on the button of Chart Elements
3. In the Data box, tick off.
4. Click the small black arrow that is next to the Databox.
5. Click more options.
6. Then switch the label option on Format Data Label pane
7. Do the data configuration by selecting the values from the cell box and choose the range you desire. Also, you only want numerical numbers deletes the x and y values boxes.

Regression analysis is a critical aspect of statistical, economic, marketing, and engineering. It is essential there essential for data analysts in these fields to learn how to do regression analysis in Excel. Running the statistics in Excel helps in understanding the statistical values in different phenomena.

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