![\"Regression](\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2014\/10\/Regression-Train-by-Roopam.jpg?resize=374%2C268\")
Regression Model Train – by Roopam<\/p><\/div>\n
This article is a continuation of our marketing analytics case study example for campaign management solutions. In this case, we started with the following\u00a0two\u00a0goals to build models to identify<\/p>\n
- \n
- Most responsive customers<\/li>\n
- Most revenue generating customers<\/li>\n<\/ol>\nProblem definition: \u00a0Part 1<\/a>\u00a0&\u00a0Part 2<\/a><\/div>\nDescription: Part 3<\/a><\/div>\nAssociation: Part 4<\/a><\/div>\nClassification: Part 5<\/a>, Part 6<\/a>,\u00a0Part 7<\/a>,\u00a0Part 8<\/a><\/div>\nEstimation: Part 9<\/a><\/div>\n
<\/h2>\n
We have accomplished the first goal through classification data mining algorithms and started with the second goal. In this part, we will continue with estimation and regression models.<\/p>\n
Regression Models & Trains<\/span><\/h2>\n
Galileo Galilei, Isaac Newton, and Albert Einstein were all proponents of determinism. The statement ‘God doesn’t play dice<\/em>‘ was Einstein’s way of saying that your life, my life and everything else in the Universe\u00a0follow predetermined paths. As a kid, my\u00a0first lesson in determinism was travelling by\u00a0Indian Railways every summer vacation to different parts of the country. All the connected passenger coaches were pulled by the driving force of the railway engine. The train was destined to follow the deterministic path of the railway track. This is the fundamental\u00a0philosophy of regression models as well.<\/p>\n
Correlation, Causation, & Coincidence –\u00a0Regression Models & Trains<\/span><\/h2>\n
![\"Source:](\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2014\/11\/correlation-causation-greek-debt-facebook.jpg?resize=358%2C267\")
<\/a>Source: businessweek.com<\/p><\/div>\n
The essential idea with regression models\u00a0is to find driving forces like the train engine and determine the path of the railway track. One of the key concepts in regression models, or science in general, is to distinguish between correlation and causation. Let’s try to understand this with our example of trains where all the connected coaches are pulled by the engine. The direction of motion of all the coaches is correlated. However, the engine is the cause of this direction. If you remove a few coaches the other coaches will still keep moving in the same direction, however, elimination of engine will bring the train to the grounding halt.<\/p>\n
In the adjacent picture, you could see the correlation between variables ‘number of babies named Ava’ and ‘housing price index’. This is most likely a spurious correlation or coincidence. \u00a0It is sort of like someone drove a car on a parallel road to the\u00a0train for a few kilometres. The car and the train will have perfect correlation for this journey, but if you will try to track the location of the train based on the position of this car then good luck to you.<\/p>\n
Case Study Example – Regression Model<\/span><\/h2>\n
Let’s come back to our case study example and create a regression model to estimate the profitability of every\u00a0customer for campaign management. In the last part<\/a>, we have created a simple regression model with a categorical variable i.e. location category for customers (small towns, medium and large cities). This time, around we will examine a continuous variable \u00a0‘profit generated by the customers in the previous quarter’ to determine the profit they will generate through campaigns.\u00a0The following is the scatter plot for these two variables:<\/p>\n
<\/p>\n
![\"Regression](\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2014\/10\/Plot-Regression-Model.jpeg?resize=640%2C391\")
<\/a>Regression Model<\/p><\/div>\n
There is a definite correlation between the above variables. If we calculate\u00a0the correlation coefficients or Carl Pearson product moment for them we get a highly significant value as displayed below:<\/p>\n
Correlation Coefficient (\u03c1)=\u00a00.372<\/pre>\n
The relationship between these two variables is mostly correlation. Profit in the previous quarter is definitely not causing profit from the campaigns. However, both these variables are governed by the same unobserved factors (driving forces) such as customers’ affinity of purchasing from the online store, and their capability to spend. Hence, this correlation is not \u00a0spurious or coincidental. As an analyst, it is absolutely important to distinguish between correlation, and coincidence through rigorous logic.<\/p>\n
Now, let’s create a simple regression model between these two variables<\/p>\n
\n\n
\n \u00a0Regression Model<\/strong><\/span><\/td>\n Estimate<\/strong><\/span><\/td>\n Std. Error<\/strong><\/span><\/td>\n t Value<\/strong><\/span><\/td>\n Pr(>|t|)<\/strong><\/span><\/td>\n<\/tr>\n \n (Intercept)<\/strong><\/td>\n 39.78<\/td>\n 0.683<\/td>\n 58.25<\/td>\n <2e-16<\/td>\n<\/tr>\n \n Profit in the Previous Quarter<\/strong><\/td>\n 0.14<\/td>\n 0.005<\/td>\n 25.96<\/td>\n <2e-16<\/td>\n<\/tr>\n \n Multiple R-squared:<\/strong><\/td>\n 0.138<\/td>\n <\/td>\n<\/tr>\n \n Adjusted R-squared:<\/strong><\/td>\n 0.138<\/td>\n<\/tr>\n \n F-statistic (P Value)<\/strong><\/td>\n 2.2E-16<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n The following is the linear equation for the above regression model<\/p>\n
\u00a0
<\/pre>\n
The model explains about 13.8% (R-square) variation in ‘profit from the campaign’.<\/p>\n
Now, let us extend this model by adding the categorical variable from the last time i.e. ‘category of the location’. Let us first create the same scatter plot with the overlay of this categorical variable.<\/p>\n
![\"Regression](\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2014\/10\/Plot-Regression-Model-by-Category.jpeg?resize=640%2C391\")
<\/a>Regression Model by Category<\/p><\/div>\n
In theory, you expect the above 3 lines for ‘location category’ to be perfectly parallel to each other. However, in practice, you will rarely find perfectly parallel (or zero interaction) lines. In our case the lines are following the same trend with very little interaction hence we can just add this categorical variable in our above model. The following is the new model\u00a0after adding ‘location category’:<\/p>\n
\n\n
\n \u00a0\u00a0Regression Model<\/strong><\/span><\/td>\n Estimate<\/strong><\/span><\/td>\n Std. Error<\/strong><\/span><\/td>\n t Value<\/strong><\/span><\/td>\n Pr(>|t|)<\/strong><\/span><\/td>\n<\/tr>\n \n (Intercept)<\/strong><\/td>\n 33.95<\/td>\n 0.686<\/td>\n 49.47<\/td>\n <2e-16<\/td>\n<\/tr>\n \n Large Cities<\/strong><\/td>\n 19.24<\/td>\n 0.634<\/td>\n 30.34<\/td>\n <2e-16<\/td>\n<\/tr>\n \n Mid-Sized Cities<\/strong><\/td>\n 7.29<\/td>\n 0.626<\/td>\n 11.64<\/td>\n <2e-16<\/td>\n<\/tr>\n \n Profit in the Previous Quarter<\/strong><\/td>\n 0.11<\/td>\n 0.005<\/td>\n 23<\/td>\n <2e-16<\/td>\n<\/tr>\n \n Multiple R-squared:<\/strong><\/td>\n 0.296<\/td>\n <\/td>\n<\/tr>\n \n Adjusted R-squared:<\/strong><\/td>\n 0.295<\/td>\n<\/tr>\n \n F-statistic (P Value)<\/strong><\/td>\n 2.20E-16<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Notice, that the adjusted R-square value for this combined model (0.295) is greater than individual continuous (0.138) or categorical (0.2065) variable regression models. This is the process of regression model development where every incremental variable inclusion in the model will improve the R-squared value.<\/p>\n
Sign-off Note<\/span><\/h4>\n
Determinism philosophy of science believes that if one has the\u00a0complete \/ absolute knowledge of the Universe then one can predict the fate of the Universe with 100% accuracy or 100% R-squared value. However, quantum mechanics has created serious doubts in the deterministic view of the Universe. Mother Nature is an enigma –\u00a0full of new tricks – this is possibly the greatest source of her eternal\u00a0beauty.<\/p>\n
See you soon with a new article.<\/p>\n","protected":false},"excerpt":{"rendered":"
This article is a continuation of our marketing analytics case study example for campaign management solutions. In this case, we started with the following\u00a0two\u00a0goals to build models to identify Most responsive customers Most revenue generating customers Problem definition: \u00a0Part 1\u00a0&\u00a0Part 2 Description: Part 3 Association: Part 4 Classification: Part 5, Part 6,\u00a0Part 7,\u00a0Part 8 Estimation:<\/p>\n