If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: AP®︎/College Statistics>Unit 5

Lesson 3: Residuals

# Calculating residual example

We look at an example scenario that includes understanding least squares regression, interpreting the regression equation, calculating residuals, and interpreting the significance of positive and negative residuals in relation to the regression line.

## Want to join the conversation?

• How do we find the residual when there are two y values for one x value?
Thanks,
~HarleyQuinn
• then we calculate the residual for both of those points separately.
• why did sal put the line right there on the graph I do not understand that
• Sal (the instructor) placed the line on the graph based on the least squares regression equation calculated from the data. This line represents the best linear approximation of the relationship between the height of the customer and the frame size of the bicycle rented. By positioning the line in this way, it provides a predictive model for estimating the frame size based on the customer's height. The goal is to minimize the overall distance between the data points and the line, capturing the general trend of the data.
(1 vote)
• At around , why didn't he add the 1/3 to 52? I guess it's not too big of a difference but wouldn't that make the residual -1 and 1/3?
Thanks,
GoldenDoodle
(1 vote)
• He already added the 1∕3 to 155∕3 to get 156∕3, which simplifies to 52.
• Where does the whole 1/3 part come in?
• The y-intercept and the slope are 1/3. The general equation for the least squares regression is

^
Y = b + mx.

where b is the why intercept and m is slope.

1/3 itself is just a preset value.
• I don't understand why he puts the line through the graph right there help!
• I'm just wondering, is this the same as Ordinary Least Squares (OLS)?
• Sort of - to be precise, OLS is a method of optimising your parameters so that the sum of the squares of the residuals is as small as possible

What if the "actual" numbers are a lot larger, like 12, or 28, or larger? I have a problem like this but when I use the equation given, I get huge numbers like 101 and 429, so when I do y-r (y-value minus residual) I get numbers like -89, which are too large to plot on my graph. What am I doing wrong?
• Where did he get the points for the graph?
(1 vote)
• Sal probably had the points before we saw the video. I think he made up these numbers.