Converting Measurement Units in Linear Regression

[@aaronhumphreys707]

Great vid!

[@caiomotta6477]

thanks man! helped me a lot

[@tunamayo21]

Hi, thank you for the video! I wonder what will happen if to beta-0 and beta-1 when we change the units for a log function. For example, instead of log(y) we change it to log (1000y)?

[@rorymc2601]

what happens if you change both variables at the same time? e.g. you start by measuring the effect of height (inches) on weight (pounds), but change to measuring height in cm and weight in kg. Because you've changed both variables, do they just cancel out and everything stays the same?

[@WadeLitt]

Thanks for the question Rory. The coefficients will be different if the relationship/conversions between the units are different. E.g. the ratio between a person who is 72 inches tall and 200 pounds has a height:weight ratio of 72/200 or 0.36. That same person is about 183 cm tall and 90 kg, a height:weight ratio of 183/90 or 2.03. So as long as you're converting one or both of the dependent/independent variable to a new type of measurement, the coefficient will change.

[@gellertturkevi-nagy1707]

Hi! Thanks for the video. If we were considering a multivariate example, when changing the units of one of the explanatory variables, would the other explanatory variables also be affected, or would they stay constant?

[@LittEconomics]

Thanks for watching Gellért! If you're only changing the units on one explanatory variable, the coefficients on all other explanatory variables will remain unchanged. This is somewhat related to the ceteris peribus component when interpreting coefficients. E.g., suppose you have the equation: y = B0 + B1*x1 + B2*x2 + B3*x3. B1 is the relationship between x1 and y, ceteris peribus (holding all other variables constant). Any given estimated coefficient of one variable is not a function of any other coefficient. Hopefully this helps a little - let me know if you have any follow up questions or whether another related video would be useful. Thanks again!