The following rearession model studies the effect of father's height on child height, where c heicht records the child's height in cmF height in records the father's height in inches, F height cm records the father's height in centimeters (1 inch-2.54 cm), andFam inc records the family's annual income in AUD.C height = B0 + B1 F height in + B2F height cm + B3Fam inc+ U Which of the following is true? a.the model suffers from multicollinearity b. the model suffers from perfect collinearityc. B1 = 2.54*B2 d. B2, = 2.54* B1
Question
The following rearession model studies the effect of father's height on child height, where c heicht records the child's height in cmF height in records the father's height in inches, F height cm records the father's height in centimeters (1 inch-2.54 cm), andFam inc records the family's annual income in AUD.C height = B0 + B1 F height in + B2F height cm + B3Fam inc+ U Which of the following is true? a.the model suffers from multicollinearity b. the model suffers from perfect collinearityc. B1 = 2.54B2 d. B2, = 2.54 B1
Solution
The model suffers from perfect collinearity. This is because F height in and F height cm are perfectly correlated as they are just different units of measurement for the same variable (father's height). This means that you can perfectly predict one from the other, which is the definition of perfect collinearity.
Also, B1 = 2.54B2 is true. This is because 1 inch equals 2.54 cm. So, if you increase father's height by 1 inch, child's height will increase by B1 units. But if you increase father's height by 2.54 cm (which is the same as increasing by 1 inch), child's height will increase by B2 units. So, B1 must be equal to 2.54B2.
The same logic applies to B2 = 2.54*B1.
So, the correct answers are: the model suffers from perfect collinearity and B1 = 2.54B2 and B2 = 2.54B1.
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