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### Course: High school statistics>Unit 4

Lesson 3: Residuals

# Introduction to residuals and least-squares regression

In linear regression, a residual is the difference between the actual value and the value predicted by the model (y-ŷ) for any given point. A least-squares regression model minimizes the sum of the squared residuals.

## Want to join the conversation?

• WHERE does the -140 +14/3x come from??
• where did -140 come from?
• That's the point at which the regression line meets the y-axis, the y-intercept.
(1 vote)
• my question is the same as the first 2 previous...Please explain
• where did you get for 140 for y
• If you extend the y-axis, the y-intercept (the point where the line first hits the y-axis) will be approximately -140. Also, the slope of the line is 14/3. So, if you transcribe the above into the equation of the line- y=mx+b, you get y=-140+14/3x
• I'm unenthused with the flow of this lesson. The first three videos are great. Calculate the residuals. Then it suddenly jumps to "as you know, the z-scores are...". The residual idea is a very basic concept that we are learning in Algebra right now. The next step needs to be to define Least Squares Regression and have them do some calculations by having their graphing calculator generate a LSRL. I wish there were a video for that. Seems to get complicated fast, preventing me from using this for basic introduction (for obvious reasons we aren't able to learn this together in the classroom right now)
• Where did the -140 and the 14/3 come from? Thank you. (time stamp: 2.27min)
• -140 + 14/3x is the equation of the linear line y^(y hat).

to dive more into it:
-140 is the y-intercept of the linear line y^
// here's how i get to that conclusion:
as you can see the line passes x-intercept at x = 30 and continues to go down. even though the continuation can't be seen but we can guess that -140 is indeed the y-intercept.

14/3 is the slope of the linear equation y^.
// here's how i get to that conclusion:
slope formula is y2-y1/x2-x1. i will use 2 points from the line: (51,100) and (30,0) => 0-100/30-51 = 100/21 = 4.7; 14/3 = 4.66667 = aprx. 4.7)
• I have the same question...how did he get -140+14/3x. If Sal calculated it before...it should be said. How am I to grasp and understand what to be done
• Did Sal pre-calculate the equation? I can't ever do it that fast!
Why are mx and b switched in places?