Shifting to Years-Since-Baseline for Modeling
Grade 9 Algebra 1 students using California Reveal Math (Unit 10: Quadratic Functions) learn to shift calendar years to a years-since-baseline variable before modeling data. The formula t = Current Year - Baseline Year converts raw years like 2018, 2019, 2020 into t = 0, 1, 2. This prevents calculator overflow when computing b^2018 in exponential models and makes the y-intercept meaningful as the value at the study start rather than a theoretical Year 0 value.
Key Concepts
Property When modeling real world data recorded in calendar years (e.g., 2015, 2016, 2017), you must define a shifted input variable $t$ so that the modeling begins at $t = 0$:.
$$t = \text{Current Year} \text{Baseline Year}$$.
The baseline year is typically the first year in your data set. Use $t$ as your input variable for all calculations and regressions.
Common Questions
Why do we shift calendar years when building regression models?
Plugging raw years like 2018 into exponential models forces the calculator to compute b^2018, causing severe rounding errors. Shifting to t = 0, 1, 2 keeps numbers small and manageable.
How do you convert calendar years to a shifted variable t?
Use t = Current Year - Baseline Year. If data starts in 2018, then 2018 becomes t=0, 2019 becomes t=1, 2020 becomes t=2. The baseline is typically the first year in the dataset.
What does the y-intercept represent in a shifted model?
The y-intercept represents the actual value at the start of the study when t=0. Without shifting, it would represent a theoretical value from Year 0, over two millennia ago.
How do you use a shifted model to make a prediction?
Find t for the target year: t = Target Year - Baseline Year. Then substitute into the model. For P(t) = 4.5t + 12 with baseline 2018, predicting 2025 uses t = 7, giving P(7) = 43.5.
What is a baseline year and how do you choose it?
The baseline year is the first year in your dataset, set as t=0. This anchors the model at the beginning of the data and makes all x-values small non-negative integers.