Plotly: what's the difference between ols and lowess trendlines

Question

I'm plotting a dataset with a trendline, but using ols vs lowess gives me significantly different line shapes. I'm sure this is an expected and perfectly normal result, but I'm afraid I don't understand the significance of the difference. Could someone explain what's going on? Here's my code using ols:

fig = px.scatter(df_small, y="Ratio",
                 trendline="ols", 
                 trendline_color_override="red")
fig.show()

And here's the plot it produced:

Using lowess gave me this plot: For context, my dataset represents the ratio of daily Covid deaths:new infections in the Province of Ontario over the previous 18 months.

Answer 1

I was curious so I looked it up:

• The first method OLS is actually Ordinary Least Squares regression so it just fits a linear regression line. It's probably not what you want in this case since it cannot fit the waves (unless you just want to show the overall trend).
• The lowess method is local polynomial regression. Since plotly 5.2.1 trendline_option is available to lowess trendlines which can make the trendline follow the underlying data more closely.

For the record I did a small test with R and ggplot2 which seems to have a better implementation:

library(ggplot2)
library(plyr)
t<-seq(0,12,.1)
noise<-rnorm(121,0,.25)
v<-cos(t)+noise
d<-data.frame(x=t,y=v)
ggplot(d,aes(x,y))+geom_point()+ geom_smooth(method="loess")