A study was conducted to monitor the emissions of a noxious substance from a chemical plant and the concentration of the chemical at a location in close proximity to the plant at various times throughout the year.A total of 14 measurements were made.Computer output for the simple linear regression least-squares fit is provided.(Some entries have been omitted and replaced with **. ) The degrees of freedom for SSM and SSE are,respectively,

A) DFM = 2 and DFE = 12.
B) DFM = 1 and DFE = 12.
C) DFM = 1 and DFE = 13.
D) DFM = 1 and DFE = 14.
E) DFM = 12 and DFE = 13.

Question

A study was conducted to monitor the emissions of a noxious substance from a chemical plant and the concentration of the chemical at a location in close proximity to the plant at various times throughout the year.A total of 14 measurements were made.Computer output for the simple linear regression least-squares fit is provided.(Some entries have been omitted and replaced with **. )

The degrees of freedom for SSM and SSE are,respectively,

A) DFM = 2 and DFE = 12.
B) DFM = 1 and DFE = 12.
C) DFM = 1 and DFE = 13.
D) DFM = 1 and DFE = 14.
E) DFM = 12 and DFE = 13.

Malekutu Mphahlele · Accepted Answer

Final Answer : B, Explanation :  The output provided states that the model has 1 degree of freedom and the error has 12 degrees of freedom. Therefore, the total degrees of freedom is 13 (1 + 12). The degrees of freedom for the regression model is always equal to the number of independent variables, which in this case is 1. Therefore, the correct answer is B: DFM = 1 and DFE = 12.

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