I am studying psychology and I have set for myself the aim to get an intuitive understanding of what I learn in stats. It worked out well in the first year however now I got to models like linear regression and feel like I don't fully understand what's going on anymore. I can perform things using software and use jargon but why it is possible to do certain things I can not really explain for myself and I really hate that !

One of the terms I can not really make sense of is "proportion of explained variance" It comes up in the context of multiple linear regression or factor analysis for example. Let's say the term indicates how much of the variance in y is explained by the predictor variable x.

Can you give me a practical example what is meant by "explained" ? I imagine sth like a column of y scores and an adjacent column of x scores. Would 100 % "explained variance" imply that when x for example doubles y doubles too or how can I imagine the relation between x and y when one talks about explained variance ?

I feel stupid and would be thankful for someone to help me with this and maybe other questions.

Cheers !