How to calculate a formula from multiple variables in Excel
Overview
Here are my notes on how to create a multivariate Linear Regression formula using Microsoft Excel and Python programs.
Vocabulary
“Loss” is how far off actual values are from the estimation function (model).
To define the total loss for a function, we want to examine the length of loss regardless of whether it’s over or under. Thus, we calculate the square of each sample loss so negative values are treated as positive.
Mean square error (MSE) is the average squared loss per example, calculated by summing up all the squared losses for individual examples, then dividing by the number of examples.
Although MSE is commonlyused, it is neither the only practical loss function nor the best loss function for all circumstances.
Obtain Sample Data
We need some sample data to build a linear regression model to provide results and a recommendation.
One is predicting expected profits from a catalog launch by a homegoods manufacturer.

Download the sample data file diamonds.csv which has 50,000 rows.
The training set contains historical data where the outcome is already known and included as a column along with the input data.
Outcome values are in the target variable (price).
NOTE: A column in a spreadsheet some call a “data field”.

The test dataset (newdiamonds.csv) contains new instances that do not have outcomes (prices) defined.
Install Excel
This tutorial assumes that you have Microsoft Excel installed.
To create a multivariate regression in Excel:
This video is from the Udacity class, about a different data setOpen in Excel
During the installation processes on Windows or MacOS, the operating system is told that suffixes at the end of file names, such as “.csv” and “.xlsx” are opened using Excel.

In Finder or doubleclick on the diamonds.csv file to open it in Excel.
Activate Analysis Toolpak

In Excel, click on the Data tab.
If Data Analysis does not appear on the far right, the Analysis Toolpak needs to be installed:
On Excel 2016, click the Tools menu at the top of the screen to select Excel Addins. Check Analysis ToolPak, then OK.
On Excel 2013, click the File menu at the top of the screen to select Properties. Check Analysis ToolPak, then OK.
The above only needs to be done once.
Data preparation
Contiguous X columns
Excel needs all variables together, so:
 Select the letter above the “caret” column to select the whole column.
 Press Ctrl+X to cut. Click on the column heading to the right of the “price” column.

Repeat for the “clarity_ord” and “cut_ord” columns.
Generate
 In Excel Data tab, Click on Data Analysis.
 If you don’t see “Data Analysis”, enable Analysis Toolpack. This only needs to be done once.

Select Regression and OK.
Conditions of attributes are in the predictor variables, also called dependent variables or (in Excel), Y Range.
 Click the red arrow icon for Y Range.
 Check “Labels”

Click in row 1 “price”. Press Commandshiftdown to select the whole column
$H$1:$H$50001
 Click the icon to collapse the popup.

Press Enter.
$I$1:$K$50001
 Click the icon to Output range.
 Cick cell N1, which leaves two blank columns.

Press Enter to accept it.

Click OK.

Variables with Pvalues (Predictionvalues) beyond .15 should not be used.
Regression equation models enable predictions to be made based on attibute values.
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 Click on the blank cell to the left of “intercept”, type = and click the Coefficient value of intercept.
 Two columns to the left of “clarity_ord”, type the input data you want an estimate for.
 Repeat this for each input.
 Click on the blank cell to the left of “intercept”, type = and click the Coefficient value of intercept.

Add a =sum() of all cells above it.

TODO: COMPLETE THIS
R Square is the percent of variance in Y that can be explained by all the X variables. 1.0 is perfect. 0.75 is the threshold for not.
Standard Error is the error of prediction expressed in the value range of Y.
Language and Theory
There are several classes that teach this topic:
Video course Multiple and Logistic Regression online class by Ben Baumer, Assistant Professor at Smith College uses a database of Italian restaurants in New York City to explore the relationship between price and the quality of food, service, and decor. Learn about logistic regression for an arbitrary number of input variables. Covered are model and predict both numeric and categorical outcomes. You’ll also learn how to fit, visualize, interpret, and compare models. Learn about the class of linear models called “parallel slopes models.” Learn to compare models so that you can select the best one. Add two, three, and even more numeric explanatory variables to a linear model.
The nice thing about datacamp’s videos is that one can highlight and copy text from videos, such as this:
ggplot(data = mpg_manuals, aes(x = factor(year), y = hwy)) + geom_boxplot()
Python Regression
Resources
 https://www.youtube.com/watch?v=O7TMCYuDbDc
 https://www.youtube.com/watch?v=HgfHefwK7VQ