Introduction to residuals and least-squares regression | AP Statistics | Khan Academy

Regression lines as a way to quantify a linear trend. Residuals at a point as the difference between the actual y value at a point and the estimated y value from the regression line given the x coordinate of that point.

AP Statistics on Khan Academy: Meet one of our writers for AP¨_ Statistics, Jeff. A former high school teacher for 10 years in Kalamazoo, Michigan, Jeff taught Algebra 1, Geometry, Algebra 2, Introductory Statistics, and AP¨_ Statistics. Today he's hard at work creating new exercises and articles for AP¨_ Statistics.

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[maheshmathe]

These are really simple to understand videos and I love to watch them any chance I get. I always feel like I am getting worth my time.

[hassanhijazi]

The take away message: "The way that we calculate this regression lines is all about minimizing the square of these residuals".
Of note, residual is the difference between the actual value (y) and the estimated value (ŷ).

[sitifathimah]

Where did you get the equation for -140 and 14/3?

[egor.okhterov]

We minimize squared error for two reasons:
1. Square is always positive. We are only interested in absolute value of errors in each point.
2. Derivative of x^2 can be easily calculated: (x^2)' = 2x.

[keganm]

WHERE DID THE -140 COME FROM AND WHERE DID THE 14 OVER 3 COME GIVE ME ANSWERS

[MsDharma]

Are we just supposed to automatically know where the "-140 +14/3" came from? Pretty sure that little bit of info would be helpful.

[goatmodegaming]

Bro I got a 2 on the AP Calculus exam but I am for sure getting a 5 on this.

[rg]

I have a doubt, how is the y' value is -140

[livinindubai]

Now I know what a linear regression is 😃

[legatha]

Khan Academy really prepares everything for my ap course...😅

[turbocpt]

The material you provide is "ok". Some things could have been improved such as not saying the Y for this particular intercept is -140. Instead show how you got -140.

[R_HeavyBones]

your videos are very nice, thank you a lot for the extra knowledge

[jenniferaucoin]

Where did -140 +14/3 come from? I am confused.

[maheshmathe]

What device do you use to make these videos?

[vusalaliyev]

Hello Sal from Germany, please make excel or accounting playlist or something new related to Economics :)

[kawaiiobama]

cool its just that i got my exam the day after tomorrow. too bad there isn't more content on this topic. 😅

[shankarkarki]

how to get the complete playlist? Can't find it.

[rachelsusan]

This is exactly why I hate math. Math teachers always just expect you to know certain aspects and don’t explain anything thoroughly. Where in the heck did the -140 and 14/3 come from??? And does anyone know where might be a better place to start learning if I’m having trouble understanding the equations??

[ChauTu]

If you are comparing height vs weight, then shouldn't the unit be in Newton as oppose to lb?

[travelsome]

fractions make it difficult to understand,