This is a simple demonstration of the meaning of least squares in univariate linear regression.
With either the intercept or the slope changing, the lines will be moving in the graph and corresponding residuals will be plotted. We can finally see the best estimate of the intercept and the slope from the residual plot.
library(animation)
par(mar = c(5, 4, 0.5, 0.1))
ani.options(interval = 0.3, nmax = 50)
## default animation: with slope changing
least.squares()
## intercept changing
least.squares(ani.type = "intercept")
We want to find an estimate for the slope in 50 candidate slopes, so we just compute the RSS one by one.
Donate
As a freelancer (currently working as a contractor) and a dad of three kids, I truly appreciate your donation to support my writing and open-source software development! Your contribution helps me cope with financial uncertainty better, so I can spend more time on producing high-quality content and software. You can make a donation through methods below.
-
Venmo:
@yihui_xie, or Zelle:xie@yihui.name -
Paypal
-
If you have a Paypal account, you can follow the link https://paypal.me/YihuiXie or find me on Paypal via my email
xie@yihui.name. Please choose the payment type as “Family and Friends” (instead of “Goods and Services”) to avoid extra fees. -
If you don’t have Paypal, you may donate through this link via your debit or credit card. Paypal will charge a fee on my side.
-
-
Other ways:
WeChat Pay (微信支付：谢益辉) Alipay (支付宝：谢益辉) 
When sending money, please be sure to add a note “gift” or “donation” if possible, so it won’t be treated as my taxable income but a genuine gift. Needless to say, donation is completely voluntary and I appreciate any amount you can give.
Please feel free to email me if you prefer a different way to give. Thank you very much!
I’ll give back a significant portion of the donations to the open-source community and charities. For the record, I received about $30,000 in total (before tax) in 2024-25, and gave back about $15,000 (after tax).