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If the relationship is `y=x₀+x₁+𝓝`, then x₀ is more strongly correlated to `y-x₁` than it is to `y` alone. This holds even if x₀ and x₁ are strongly correlated
by mortehu 8y ago
If the relationship is `y=x₀+x₁+𝓝`, then x₀ is more strongly correlated to `y-x₁` than it is to `y` alone. This holds even if x₀ and x₁ are strongly correlated, as long as they're not 100% correlated.
- chronial 8y agoIf y = x_0 and x_1 = x_0 + N, then y = x_1 - N. Then y and x_1 are highly correlated. But y - x_0 = 0 – which is not correlated to x_1 at all. y is "success" x_0 is "socioeconomic background" x_1 is "result of the marshmallow test"
- mortehu 8y agoThe question isn't whether you can produce absurd example models where "What [vanderZwan says] would only be true if character traits and socioeconomic background were uncorrelated", it's whether it holds in general.