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:

Lith/o

A prefix in medical terminology meaning "stone," often used to describe conditions related to the formation of calculi or stones in the body, such as lithotripsy.

Olig-

A prefix denoting few or scanty, often used in medical and scientific terms.

Lithotripsy

A medical procedure that uses shock waves or a laser to break down stones in the kidney, bladder, or urinary tract into smaller pieces that can be passed naturally.

Polyuria

The production of abnormally large volumes of dilute urine, which can be a symptom of various conditions, including diabetes insipidus and diabetes mellitus.