# Meaning of Intercept and what the intercept should be with no measurement error?

I'm going into University this year, Engineering to be more specific and I was given an assignment over the summer about regression. (Something I have no knowledge about) Basically, in my questions I have two questions that I have no idea about answering. Here they are...

1. I need to describe the significance of the intercept. In my thing on excel I have a few different kinds from what I can see. Theres an image attached so you can see. I have things like "Coefficient, t Stat, P-value..." Whats the significance of the intercept? For this assignment its basically about finding the Total Energy, Total Charge, Power, and I^2 (By the way, what would you call I^2?) from the elapsed time, Voltage, and Current in a series circuit. I highlighted in blue the intercept and standard error in the image

2. This one is hard, I cannot find anything to help me...What should the intercept be if there are no measurement errors?

Please any help will be appreciated!

• You should add the self-study tag as this is homework. Have you read any simple explanations of linear regression, such as this? Have you plotted the data used for each regression to see what they look like? That might help illuminate these concepts. – EdM Sep 3 '15 at 21:50

There are two relationships in mathematics that unfortunately have their terminology often mixed up. A linear relationship is governed by an equation of the form:

$$y = a \cdot x.$$

An affine relationship is governed by an equation of the form:

$$y = a \cdot x + b.$$

The intercept in the affine equation is $b$. Of course, if $y$ has a linear relationship with $x$, it also has an affine relationship with $x$ (with $b$ = 0). Certain things in life/nature truly have linear relationships, for example,

• $y =$ length of an object measured in inches
• $x =$ length of an object measured in feet

$$y = 12 \cdot x.$$

Unfortunately, linear regression typically refers to finding the affine relationship which "best" describes the data. If we had some error in our measurements, and ran a linear regression, we might get results like:

$$y = 12.1 \cdot x - 1.25.$$

I hope this was helpful. I didn't want to address the question too directly. Let me know if you have any questions.

PS: Did it say statistical significance or just significance in (1)?

• Thank you for taking the time to answer, it asked for "physical significance" if that helps – John Sep 3 '15 at 16:39
• I'm assuming it has to be with the series circuit itself. So what significance it would have on the circuit but that seems weird. (But I may be wrong) – John Sep 3 '15 at 16:41