To Test Whether or Not the Population Regression Function Is $R ^ { 2 }$

question 36

Short Answer

To test whether or not the population regression function is linear rather than a polynomial of order r, a. check whether the regression $R ^ { 2 }$ for the polynomial regression is higher than that of the linear regression.
b. compare the TSS from both regressions.
c. look at the pattern of the coefficients: if they change from positive to negative to positive, etc., then the polynomial regression should be used.
d. use the test of $( r - 1 )$ restrictions using the $F$ -statistic.

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Definitions:

Illusory Correlation

The perception of a relationship between two variables when no such relationship exists or the perception is stronger than the actual relationship.

Hypothesis

A proposed explanation for a phenomenon, made as a starting point for further investigation, that can be tested through experimentation and observation.

Casual Impressions

Refers to the informal and intuitive judgments we make about others.

Correlation Coefficients

Statistical measures expressing the extent to which two variables move in relation to each other, ranging from -1 to 1.