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What does the normal probability density function describe?
A probability density function (pdf) for a continuous random variable (RV), is a function that describes the probability that the RV random variable will fall within a range of values. The probability of the RV falling between two values is the integral of the relevant PDF. The normal or Gaussian distribution is one of the most common distributions in probability theory. Whatever the underlying distribution of a RV, the average of a set of independent observations for that RV will by approximately Gaussian.
What is the difference between interpolation and extrapolation?
Both, interpolation and extrapolation are used to predict, or estimate, the value of one variable when the value (or values) of other variable (or variables) is known. This is done by extending evaluating the underlying function. For interpolation, the point in question is within the domain of the observed values (there are observations for greater and for smaller values of the variables) wheres for extrapolation the point in question is outside the domain.
When can the standard error of the estimate be used to construct a prediction interval about a value y'?
You need the data to be homoscedastic, the errors to be independent. The independent variable(s) should lie within (or very close to) the range of observed values.
What does variable held constant mean?
The distinction between these two types of variables is whether the variable regress on another variable or not. Like in a linear regression the dependent variable (DV) regresses on the independent variable (IV), meaning that the DV is being predicted by the IV. Within SEM modelling this means that the exogenous variable is the variable that another variable regresses on. Exogenous variables can be recognized in a graphical version of the model, as the variables sending out arrowheads, denoting which variable it is predicting. A variable that regresses on a variable is always an endogenous variable even if this same variable is used as an variable to be regressed on.
Is hair color a discrete or continuous variable?
Hair color is considered a discrete variable because it falls into distinct categories such as blonde, brown, black, red, etc. Each category is separate and distinct from the others, with no intermediate shades. In contrast, a continuous variable would have an infinite number of possible values within a range, which is not the case with hair color.
