Additive Model
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When a time series displays a linear relationship, we can use an additive regression model to forecast.
With regressions for time series, time is (one of) the predictor variable(s).
For example... "Every X periods, our response variable +/- by Y units."
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.
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.
b0 = 1029.23
b1 = 43.89
y-hat = 1029.23 + 43.89(x1)
For Year 15, we can predict 1687.58 Tinder matches.
y-hat = 1029.23 + 43.89(15)
y-hat = 1029.23 + 658.35
y-hat = 1687.58
