{"id":5782,"date":"2015-07-12T13:05:29","date_gmt":"2015-07-12T07:35:29","guid":{"rendered":"http:\/\/ucanalytics.com\/blogs\/?p=5782"},"modified":"2017-07-08T10:37:47","modified_gmt":"2017-07-08T05:07:47","slug":"how-effective-is-my-marketing-budget-regression-with-arima-errors-arimax-case-study-example-part-5","status":"publish","type":"post","link":"https:\/\/ucanalytics.com\/blogs\/how-effective-is-my-marketing-budget-regression-with-arima-errors-arimax-case-study-example-part-5\/","title":{"rendered":"How Effective is My Marketing Budget? – Regression with ARIMA Errors, Case Study Example (Part 5)"},"content":{"rendered":"
\n

So far we have covered the following topics in this case study example\u00a0on time series forecasting and ARIMA models:<\/p>\n

Part 1<\/a>\u00a0: Introduction to time series modeling & forecasting<\/div>\n
Part 2<\/a>: Time series decomposition to decipher patterns and trends before forecasting<\/div>\n
Part 3<\/a>: Introduction to ARIMA models for forecasting<\/div>\n

Part 4<\/a>: ARIMA model case study example<\/p>\n

These topics\u00a0focused on forecasts\u00a0using embedded information in the data series. These forecasts are often regarded as good-to-know information and are quite useful for planning purposes. However,\u00a0they don’t empower organizations with information to change the course of the future.Organizations usually like to know if they could do things better for\u00a0improved outcomes. They also like to know if their current efforts are generating desired outcomes, and want suggestions for course corrections. These are part of \u00a0fundamental questions for any organization and require thorough analysis and creativity.<\/p>\n

\"Exogenous<\/a>Keeping with this theme, in this article, we will continue with our case study example and try to answer the question whether the PowerHorse tractors marketing effort is generating added sales revenue. For this, we will use regression with ARIMA errors (ARIMAX) or exogenous variable ARIMA. Before that let’s learn about a useful concept for model selection\u00a0i.e. Akaike Information Criterion (AIC) through:<\/p>\n

Balancing Acts<\/span><\/h2>\n

Michael Jackson, the king of pop music,\u00a0is regarded as one of the most famous and truly international artists till date. His net earning from the\u00a0sales of his music albums\u00a0had surpassed his peers by a huge margin. Despite this when he died in 2009 he had close to $400 million in debts. Clearly, he could not manage his finances. Elves Presley, another legendary musician, met\u00a0the same fate when he died. Just before their deaths both these artists were working relentlessly for their stage performances to fight their financial troubles. Clearly, healthy finance is not just about earning well but it is also about managing costs. It’s a fine balancing act between these two parameters as depicted by the following simple equation:<\/p>\n

Debt\u00a0= Cost – Income<\/span><\/p><\/blockquote>\n

For healthy finances, the idea is to keep the debt at the minimum. Model development in data science, like any other endeavor in life, is also about finding the right balance. We will explore the same in the next section while learning about…<\/p>\n

Akaike Information Criterion (AIC)<\/span><\/h2>\n

Akaike Information Criterion (AIC) is a mechanism to select the best fit model. AIC has similarities with the debt\u00a0formula we have seen in the previous section. AIC is an effort to balance the model between goodness-of-fit and\u00a0number of parameters used in the model. This is similar to the balancing act between income and cost. As a modeler, you care about the maximum\u00a0goodness of fit (income) with the minimum number of parameters (cost). The formula for AIC is displayed below:<\/p>\n

\"AIC=2K-2ln(L)<\/p><\/blockquote>\n

For the given model, L\u00a0in the above formula is the maximized value of the likelihood function representing goodness-of-fit, and\u00a0k<\/i>\u00a0the number of estimated parameters. Like your debts, you want to keep AIC value at the minimum to choose the best possible model.\u00a0Bayesian Information Criterion (BIC) is another variant of AIC and is used for the same purpose of best fit model selection. For the best possible model selection, you want to look at AIC, BIC, and AICc (AIC with sample correction) if all these values are minimum for a given model<\/p>\n

Regression with ARIMA Errors – Case Study Example<\/span><\/h2>\n

For the last 4 years, PowerHorse tractors is \u00a0running an expensive\u00a0marketing and farmer connect program to boost their sales. They are interested in learning the impact of this program on overall sales. As a data science consultant you are helping them with this effort. This is an interesting problem and requires a thorough analysis followed by\u00a0creative solutions and scientific monitoring mechanism. To begin with you will build models based on regression with ARIMA errors and compare them with the pure play ARIMA model. This analysis will provide some clues towards effectiveness of the marketing program. However, this analysis will not be conclusive for finding shortcomings and enhancements for the program which will require further analysis and creative solutions. The later analysis will become another case study example on YOU CANalytics. The following is the approach you have taken for\u00a0regression with ARIMA errors. If you want a quick brush up on regression before you jump to regression with ARIMA errors read the following articles<\/p>\n