Insertion symbol

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Last seen on: –Thomas Joseph – King Feature Syndicate Crossword – Aug 2 2022
Eugene Sheffer – King Feature Syndicate Crossword – Apr 9 2021
Thomas Joseph – King Feature Syndicate Crossword – Nov 2 2020

Random information on the term “Insertion symbol”:

The hat operator is a mathematical notation with various uses in different branches of science and mathematics.

In statistics, the hat matrix H projects the observed values y of response variable to the predicted values ŷ:

In screw theory, one use of the hat operator is to represent the cross product operation. Since the cross product is a linear transformation, it can be represented as a matrix. The hat operator takes a vector and transforms it into its equivalent matrix.

For example, in three dimensions,

In statistics, the hat is used to denote an estimator or an estimated value. For example, in the context of errors and residuals, the “hat” over the letter ε indicates an observable estimate (the residuals) of an unobservable quantity called ε (the statistical errors). In simple linear regression with observations of independent variable data x i {\displaystyle x_{i}} and dependent variable data y i {\displaystyle y_{i}} , and assuming a model of y i = β 0 + β 1 x i + ε i {\displaystyle y_{i}=\beta _{0}+\beta _{1}x_{i}+\varepsilon _{i}} , can lead to an estimated model of the form y ^ i = β ^ 0 + β ^ 1 x i {\displaystyle {\hat {y}}_{i}={\hat {\beta }}_{0}+{\hat {\beta }}_{1}x_{i}} where ∑ i ( y i − y ^ i ) 2 {\displaystyle \sum _{i}(y_{i}-{\hat {y}}_{i})^{2}} is minimized via least squares by finding optimal values of β ^ 0 {\displaystyle {\hat {\beta }}_{0}} and β ^ 1 {\displaystyle {\hat {\beta }}_{1}} for the observed data.

Insertion symbol on Wikipedia

Random information on the term “CARET”:

The caret (/ˈkærɪt/) is a V-shaped grapheme, usually inverted and sometimes extended, used in proofreading and typography to indicate that additional material needs to be inserted at this point in the text.

A similar mark has a variety of unrelated uses in programming, mathematics and other contexts. The symbol ^ was included in typewriter and computer keyboards so that circumflex accents could be overprinted on letters (as in ŵ). This facility is not provided as standard on typical US keyboard settings and so the character became reused in computer languages for many other purposes. The misnomer “caret” is frequently applied to the circumflex symbol in that context, because of its similarity to the proofreading mark for insertion. This page will call this symbol a “circumflex” to distinguish it from a true caret. This circumflex is not to be confused with other chevron-shaped characters, such as the circumflex accent, the turned v or the logical AND, which may occasionally be called carets.

CARET on Wikipedia