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Mean Squared Error (MSE) Here's what I randomly found on course online (Google Course, Andrew NG, etc.) about Mean Squared Error (MSE)

  1. prediction - actual or actual - prediction, It's maybe identical by squared but I never see anyone write F = am instead of F = ma before. Why it's so random swap? (I just curious)
  2. The hat -, ~, ^ all are same? (This look like no standard at all?)
  3. Some use regular (i),some used sub i, some used super i or (i)

What's actual standard formula I can rely on?

katopz
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  • You should try to understand the differences in these formulas as a matter of context. Different authors may use different variables for the observed values and for the "predicted" (fitted) values. The sum of squares of errors appears in all the formulas, as does the division by the number of observations. Whether any of these formulas is exactly what you want depends on what your are trying to do. – hardmath Feb 11 '19 at 04:01
  • "Mean squared error" refers to various similar quantities that depend on the context. Since the quantities have different meanings in different contexts, the notation used to denote them will vary as well. – angryavian Feb 11 '19 at 04:01

1 Answers1

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"prediction - actual or actual - prediction, It's maybe identical by squared but I never see anyone write F = am instead of F = ma before. Why it's so random swap? (I just curious)"

The reason noone writes $F=am$ is because $F$ and $a$ are vectors and by convention, you start by the constants ($m$ here), then you add the vector. It's not a random swap, it's just that there is no convention for that, both writing exist.

"The hat -, ~, ^ all are same?" (This look like no standard at all?) Yes, they are all the same, there is no global standard.

"Some use regular (i),some used sub i, some used super i or (i)" The superscript i is applied on specific point $x^i$ while the subscript is applied on the actual value taken by the function $Y$. Some books write $x_i$ or $x_i$ but I have never seen $Y^i$.

"What's actual standard formula I can rely on?" Anyone you like.

PackSciences
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