A company that manufactures computer chips wants to use a multiple regression mo

Question

A company that manufactures computer chips wants to use a multiple regression model to study the effect that the variables

df for the regression sum of squares =

df for the error sum of squares =

df for the total sum of squares =

A company that manufactures computer chips wants to use a multiple regression model to study the effect that the variables

daily production volume (in 's of units)
daily amount of time involved in production (in hours)

have on

total daily production cost (in 's of dollars).

If a regression model is estimated using observations on each of these variables, what are the degrees of freedom (df) for theregression sum of squares, error sum of squares, and the total sum of squares?

Explanation / Answer

y is the response variable

and the two predictor variables are x1 and x2.

there are n=103 observations

the regression equation of y on x1 and x2 is

Y=a1+a2*x1+a3*x2 where Y is the predicted value of y and a1,a2,a3 are the parameters.

so there are p=3 parameters that are needed to be estimated.

now df for the total sum of squares is always=total observations-1

so here the df is=n-1=103-1=102 [answer]

df for the regression sum of squares is always=number of parameters to be estimated-1

so here df is=p-1=3-1=2 [answer]

and we know

df(regression)+df(error)=df(total)

hence df for the error sum of squares=df for the total sum of squares-df for the regression sum of squares=102-2=100 [answer]

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