RESEARCH METHODOLOGY

STATISTICAL TECHNIQUES AND TOOLS

CORRELATION COEFFICIENT COEFFICIENT OF DETERMINATION

Question [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
How do you calculate a residual?
A
Observed-Predicted
B
Predicted-Observed
C
Either A or B
D
None of the above
Explanation: 

Detailed explanation-1: -Definition. The residual for each observation is the difference between predicted values of y (dependent variable) and observed values of y . Residual=actual y value−predicted y value, ri=yi−^yi.

Detailed explanation-2: -Residuals are differences between the one-step-predicted output from the model and the measured output from the validation data set. Thus, residuals represent the portion of the validation data not explained by the model.

Detailed explanation-3: -If the points show no pattern, that is, the points are randomly dispersed, we can conclude that a linear model is an appropriate model. If the points show a curved pattern, such as a U-shaped pattern, we can conclude that a linear model is not appropriate and that a non-linear model might fit better.

Detailed explanation-4: -A residual is calculated by taking an individual’s observed y value minus their corresponding predicted y value. Therefore, each individual has a residual. The goal in least squares regression is to construct the regression line that minimizes the squared residuals.

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