How many degrees of freedom are in the following situations assuming that the nu

Question

How many degrees of freedom are in the following situations assuming that the number of data points in each case is 24?

You are asked to run a second order polynomial fit on the data. You are asked to find the standard error of the average, assuming population statistics. You are asked to fit the data to a linear trendline. You are asked to find the uncertainty in each data point assuming sample statistics. You are attempting to fit the data using the method of least squares to the following form. y=A*2.7-Bx*cos(Cx + D) + E

Explanation / Answer

1) You are asked to run a second order polynomial fit on the data.

In this case there are three parameters so degrees of freedom = 24 - 3 = 21

2)You are asked to find the standard error of the average, assuming population statistics.

Here degrees of freedom = n - 1 = 23 because one degrees of freedom(df) loss due to sample mean .

3) You are asked to fit the data to a linear trendline

In this case there are only two parameters a(intercept and b(slope) so df = 24 - 2 = 22

There are 5 parameters as A, B, C, D and E so df = 24 - 5 = 19

5) You are attempting to fit the data using the method of least squares to the following form. y=A*2.7-Bx*cos(Cx + D) + E

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