# How can I interpret a regression statistics table in Excel?

Oct 20, 2015

I assume you mean this:

The "Coefficients" are the slope or y-intercept in this case. "HH SIZE" refers to the Slope, and of course, Intercept is the y-intercept.

If you multiply the Standard Error by $1.96$, you get the Associated Error for either the Intercept or the Slope. The Associated Error is basically the uncertainty you have.

For example, in a standard physics lab course, bare minimum, here's what you would need to know:

• Slope
• Intercept
• Slope Standard Error ($S {E}_{\text{slope}}$)
• Slope Associated Error ($A {E}_{\text{slope}}$)
• Intercept Standard Error ($S {E}_{\text{int}}$)
• Intercept Associated Error ($A {E}_{\text{int}}$)

The sample standard deviation is:

$s = \sqrt{\frac{1}{N - 1} {\sum}_{i = 1}^{N} {\left({x}_{i} - \overline{x}\right)}^{2}}$

where $N$ is the number of trials, ${x}_{i}$ is each individual value, and $\overline{x}$ is the average of said values.

The Standard Error is:

$S E = \frac{s}{\sqrt{N}}$

where $s$ is the standard deviation above, and:

$A E = 1.96 \cdot S E$

Here is an example of an Ohm's law analysis I did using a similar regression statistics table:

Oftentimes, even in a quantitative analysis course, you only need to further know the coefficient of determination ${R}^{2}$. The closer it is to $1$, the better it is, but it is only for a linear fit line.

Other than that, I have not had to use any other quantity on the regression statistics table in my 7 University semesters.
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