Multiplicative Model

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

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 = e^{6.0281 + 0.0793(x₁)}

For Year 15, we can predict 1363.21 Tinder matches.

y-hat = e^{6.0281 + 0.0793(15)}
y-hat = e^{6.0281 + 1.1895}
y-hat = e^7.2176
y-hat = 1363.21