I'm a physiologist by profession. I've conducted a research study that examines the effect of altitude on sustainable power output (let's call this variable CP) in cycling. A 3rd order polynomial nicely characterizes the relationship between altitude and percentage decrease in sustainable power in the range 0 - 4300 m
$$y = ax^3 + bx^2 + cx + d.$$
where $y$ is percent of sea level CP, and $x$ is the altitude in km.
The percent decline in CP though also depends on the baseline level ie: sea level CP. People with higher CP at sea level tend to have a greater decline at altitude. So this acts like a covariate.
Is there a way to include this covariate such that a single function incorporates the effect of both the altitude and the baseline (sea level) value?
Multiple linear regression should do the job. Let $X_1$ be the latitude, $X_2$ the sea level and $Y$ the CP, so a possible model is $$ y=\beta_0 + \beta_1x_1 + \beta_2x_1^2 + \beta_3x_1^3 + \beta_4x_2 + \epsilon . $$ You can start by assuming that $\epsilon \sim \mathcal{N}(0, \sigma^2)$ and estimating the coefficients $\beta_i$ by the OLS method.