线性回归是否适用于分类自变量和连续因变量？

Question

I have a dataset where:

X1 - categorical independent variable

X2 - continuous independent variable

y - continuous dependent variable

And I'm looking to use X1 and X2 to predict y. Is linear regression appropriate for this (does it even make sense to regress over a categorical independent variable?)? If so, how can I use linear regression when X1 is a categorical independent variable (eg eye colour)?

Should I create a separate linear regression model for each of the categories in X1? Or try to create a multiple linear regression model?

Taking a look online there are mostly resources concerning continuous independent -> continuous dependent (linear regression), or continuous independent -> categorical dependent (logistic regression).

Would appreciate being pointed to any resources/tools that could help me.

Answer 1

You can use linear regression, but you first need to first encode X1 as a series of variables.

Here's a simple example, using the 'dummy coding' method:

┏━━━━━━━━━━━━┳━━━━━┳━━━━━┓
┃ Eye Colour ┃ x11 ┃ x12 ┃
┣━━━━━━━━━━━━╋━━━━━╋━━━━━┫
┃ Blue       ┃  0  ┃  0  ┃
┣━━━━━━━━━━━━╋━━━━━╋━━━━━┫
┃ Brown      ┃  1  ┃  0  ┃
┣━━━━━━━━━━━━╋━━━━━╋━━━━━┫
┃ Green      ┃  0  ┃  1  ┃
┗━━━━━━━━━━━━┻━━━━━┻━━━━━┛

Here's an article that explains different coding methods:

https://stats.idre.ucla.edu/spss/faq/coding-systems-for-categorical-variables-in-regression-analysis-2/