What about the covariance formula makes it obvious that it is about 'linear' associations?
38969
Why does Covariance measure only Linear dependence?
33843
Assumption Of Linear Regression
34036
Positive correlation and negative regressor coefficient sign
21808
Does correlation assume stationarity of data?
77307
Why does inversion of a covariance matrix yield partial correlations between random variables?
154994
Violation of linearity assumption in Logistic Regression
114717
What does goodness of fit mean in context of linear regression
52129
covariance of increasing functions
45866
How to infer correlations from correlations
121494
Invariance, covariance and symmetry
9381
How to derive variance-covariance matrix of coefficients in linear regression
35178
Covariance of order statistics (uniform case)
9356
Derivation of the formula for Ordinary Least Squares Linear Regression
6293
Is there a way to use the covariance matrix to find coefficients for multiple regression?
141134
How to calculate weighted covariance?
155765
How to derive the covariance matrix of $\hat\beta$ in linear regression?
62510
Explanation of linearity of expectation