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Exercise

Forecasting sales allowing for advertising expenditure

Welcome to the last chapter of the course!

The auto.arima() function will fit a dynamic regression model with ARIMA errors. The only change to how you used it previously is that you will now use the xreg argument containing a matrix of regression variables. Here are some code snippets from the video:

> fit <- auto.arima(uschange[, "Consumption"],
                    xreg = uschange[, "Income"])

> # rep(x, times)
> fcast <- forecast(fit, xreg = rep(0.8, 8))

You can see that the data is set to the Consumption column of uschange, and the regression variable is the Income column. Furthermore, the rep() function in this case would replicate the value 0.8 exactly eight times for the matrix argument xreg.

In this exercise, you will model sales data regressed against advertising expenditure, with an ARMA error to account for any serial correlation in the regression errors. The data are available in your workspace as advert and comprise 24 months of sales and advertising expenditure for an automotive parts company. The plot shows sales vs advertising expenditure.

Think through everything you have learned so far in this course, inspect the advert data in your console, and read each instruction carefully to tackle this challenging exercise.

Instructions

100 XP
  • Plot the data in advert. The variables are on different scales, so use facets = TRUE.
  • Fit a regression with ARIMA errors to advert by setting the first argument of auto.arima() to the "sales" column, second argument xreg to the "advert" column, and third argument stationary to TRUE.
  • Check that the fitted model is a regression with AR(1) errors. What is the increase in sales for every unit increase in advertising? This coefficient is the third element in the coefficients() output.
  • Forecast from the fitted model specifying the next 6 months of advertising expenditure as 10 units per month as fc. To repeat 10 six times, use the rep() function inside xreg like in the example code above.
  • Plot the forecasts fc and fill in the provided code to add an x label "Month" and y label "Sales".