Question

1. Please explain what regression analysis is – include in your answer a statement about how predictor and criterion variables are used, as well as an explanation of what beta-weights are. Also, please provide an original example of multiple regression (you must explicitly state what your predictor and criterion variables are).

Answer 1

Regression analysis is a set of statistical processes for estimatingthe relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variableand one or more independent variables (or 'predictors'). More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'criterion variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed

Predictor variable is the name given to an independent variable used in regression analyses. The predictor variable provides information on an associated dependent variable regarding a particular outcome

Criterion Variable

In regression analysis (such as linear regression) the criterion variable is the variable being predicted. In general, the criterion variable is the dependent variable.

​​​​Beta weights

A beta weight is a standardized regression coefficient (the slope of a line in a regression equation). They are used when both the criterion and predictor variables are standardized (i.e. converted to z-scores).

A beta weight will equal the correlation coefficient when there is a single predictor variable. β can be larger than +1 or smaller than -1 if there are multiple predictor variables and multicollinearity is present.

If the independent/dependent variables are notstandardized, they are called B weights. B weights aren’t as useful as β-weights because cross-comparisons of different units are only possible if they are standardized.

Example for multiple regression

The problem of predicting weight reduction(criterion variable) in form of number of KGs reduced, hypothetically, could depend upon input features such as age, height, weight of the person and the time spent on exercises(predictor variables)