Multiplicative Model

When a time series displays an exponential relationship, we can use an multiplicative regression model to forecast.

Scenario: Given the Tinder stats for Crammer Nation University's Delta Apple Pi chapter, interpret the resulting regression equation and find the predicted Tinder Matches for Year 15.

Since the scatterplot doesn't resemble a linear relationship, we must transform it!

To transform an exponential relationship to a linear relationship (to be able to run regression on it)... we'll take the natural logarithm (ln) of the response variable.

y-hat is the predicted value ("Tinder matches") given an x1 value ("Year").
b0 is the y-intercept.
b1 is the change in predicted response ("Tinder matches") for each unit +/- in x1 ("Year").
x1 is the value for the first (i.e. "1") predictor variable.

Taking the natural logarithm (ln) of y-hat means that technically, y-hat itself equals...

...which we can rewrite like so:

This is the "multiplicative" model since we're essentially multiplying each component (eb0 and eb1x1) of the regression!

b0 = 6.0281
b1 = 0.0793

y-hat = e6.0281 + 0.0793(x1)

For Year 15, we can predict 1363.21 Tinder matches.

y-hat = e6.0281 + 0.0793(15)
y-hat = e6.0281 + 1.1895
y-hat = e7.2176
y-hat = 1363.21

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