,
measures the proportion reduction in the variation of Y achieved by the
introduction of the entire set of X variables considered in the model.
Outlier - An extreme value in the dependent (response) variable. Compared with a leverage point, which is an extreme value in the independent (explanatory) variables.
Parameter - Generally, it is either a boundary or limit ,or an element or a characteristic.
Partial Correlation - Correlation between two variables given that the linear effect of one or more other variables has been controlled. Example. r12.3 is the correlation of variables one and two given that variable three has been controlled.
Partial Correlation Coefficients - This is the square root of a coefficient of partial determination. It is given the same sign as that of the corresponding regression coefficient in the fitted regression function.
Partial Determination
Coefficients- This measures the marginal contribution of one X variable when
all others are already included in the model. In contrast, the coefficient of
multiple determination,
,
measures the proportion reduction in the variation of Y achieved by the
introduction of the entire set of X variables considered in the model.
Partial Regression Coefficient, Partials - In a multiple regression equation, the coefficients of the independent variables are called partial regression coefficients because each coefficient tells only how the dependent variable varies with the selected independent variable.
Partial Slope Coefficient - See Partial Regression Coefficient.
Pearson’s Sample Correlation Coefficient, r - Measures the strength of linear association between two numerical variables.
Population - A group of people that one whishes to describe or generalize about.
Predictor Variable, Independent Variable, Explanatory Variable, Input Variable - The variable in correlation or regression that can be controlled or manipulated. In math, x frequently represents the independent variable.
Prediction Equation - An equation that predicts the value of one variable on the basis of knowing the value of one or more variables. Note: Formally prediction equation is a regression equation that does not include an error term.
Prediction Interval - In regression analysis, a range of values that estimate the value of the dependent variable for given values of one or more independent variables. Comparing prediction intervals with confidence intervals: prediction intervals estimate a random value, while confidence intervals estimate population parameters.
Population Parameter, Parameter - A measurement used to quantify a characteristic of the population. Even when the word population is not used with parameter, the term refers to the population. Example: The population mean is a measure of central tendency of the population. The population parametric is usually unknown. (See Sample Statistic.)
Proportional Reduction of Error (PRE) - A measure of association that calculates how much more you can reduce your error in the predication of y if you know x, then when you do not know x. Pearson’s r is not a PRE, but r-squared is a PRE.
Positive Correlation- This relationship occurs whenever the dependent variable increases as the independent variable increases
P-values, Observed Significance Level - The probability of making a Type I error. (i.e. given that the null is true, the probability of getting a data set like the one we have or one more extreme in the direction of the alternative.)
r, Correlation Coefficients, Pearson’s r - Measures the strength of linear association between two numerical variables.
R, Coefficient of Multiple Correlation - A measure of the amount of correlation between more than two variables. As in multiple regression, one variable is the dependent variable and the others are independent variables. The positive square root of R-squared.
r2 , r-squared (r-sq.), Coefficient of Simple Determination - The percent of the variance in the dependent variable that can be explained by of the independent variable.
R-squared, Coefficient of Multiple
Determination -
The percent of the variance in the dependent variable that can be
explained by all of the independent variables taken together.
R-Squared Adjusted (R-sq. adj.), Adjusted R-Squared - A version of R-Squared that has been adjusted for the number of predictors in the model. R-Squared tends to over estimate the strength of the association especially if the model has more than one independent variable.
Range of Predictability, Region of Predictability - The range of independent variable(s) for which the regression model is considered to be a good predictor of the dependent variable. For example, if you want to predict the cost of a new space vehicle subsystem based on the weight, and all of the input data subsystem weights all range from 100 to 200 pounds. You could not expect the resulting model to provide good predictions for a subsystem that weighs 3000 pounds.
Regression Analysis, Statistical Regression, Regression - Methods of establishing an equation to explain or predict the variability of a dependent variable using information about one or more independent variables. The equation is often represented by a regression line, which is the straight line that comes closest to approximating a distribution of points in a scatter plot. When "regression" is used without any qualification it refers to “linear” regression.
Regression Artifact, Regression Effect - An artificial result due to statistical regression or regression toward the mean.
Regression Curve - The curve that represents the regression model.
Regression Coefficient, Regression Weight - In a regression equation the number in front of an independent variable. For example, if the regression equation is Y = mx + b then m is the regression coefficient of the x-variable. The regression coefficient estimates the effect of the independent variable(s) on the dependent variable. (Compare with Partial Regression Coefficients)
Regression Constant - Unless specified otherwise, the regression constant is the intercept in the regression equation.
Regression Equation - An algebraic equation that models the relationship between two (or more) variables. If the equation is Y = a + bX + e, then Y is the dependent variable, X is the independent variable, b is the coefficient of X, and a is the intercept, and e is the error term (See Prediction Equation).
Regression Line, Trend Line - When the best fitting regression model is a straight line, that line is called a regression “line.” Ordinary Least Squares method is usually used for computing the regression line.
Regression Model - An equation used to describe the relationship between a continuous dependent variable, an independent variable or variables, and an error term.
Regression Plane - When the regression model has two independent variables, then a plane represents the relationship between the variables two-dimensional. Example: z = a + bx + cy
Regression Plot- A scatterplot with the regression curve on the same graph.
Regression SS (also SSR or SSregression) - The sum of squares that is explained by the regression equation. Analogous to between-groups sum of squares in analysis of variance.
Regression Toward the Mean - The type of bias described by Francis Galton, a 19th century researcher. A tendency for those who score high on any measure to get somewhat lower scores on a subsequent measure of the same thing- or, conversely, for someone who has scored very low on some measure to get a somewhat higher score the next time the same thing is measured. Knowing how much regression toward the mean there is for a particular pair of variables gives you a prediction. If there is very little regression, you can predict quite well. If there is a great deal of regression, you can predict poorly if at all. (See Vogt, page 240)
Regression Weight, Regression Coefficient - In a regression equation the number in front of an independent variable. For example, if the regression equation is Y = mx + b then m is the regression coefficient of the x-variable. The regression coefficient estimates the effect of the independent variable(s) on the dependent variable. (Compare with Partial Regression Coefficients)
Regress On - The dependent variable is “regressed on” the independent variable(s). We will regress the cost of the space vehicle (based) on the weight of the vehicle. If x predicts y, then y is regressed on x. (i.e. Regress the dependent variable on the independent. Response variable is regressed on the explanatory variable.)
Rejection Region - The area in the tail(s) of the sampling distribution for a test statistic. The figure below shows the Rejection Region in red.
Residuals, Errors - The amount of variation on the dependent variable not explained by the independent variable.
Response Variable- Same as the independent variable.
Robust - Said of a statistic that remains useful even when one or more of the assumptions is violated.
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