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Interpreting computer regression data

AP.STATS:
DAT‑1 (EU)
,
DAT‑1.G (LO)
Interpreting computer generated regression data to find the equation of a least-squares regression line. Predictors and coefficients. S and R-squared.

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• In this case, how to interpret the values of T and P?

• T (which you will find as "t" in R language summary function results) is the coefficient divided by the standard error. A large t value means that it is very likely that the coefficient will be significant. You should generally keep in your regression model those variables with a large absolute value in this field.
P (which you will find as "Pr(>|t|)" in R's summary function results) is a measure of how likely it is that your coefficient will be zero for the corresponding variabie. You will generally prefer to keep in your model those variables with a low value in this field.
Hope you find it useful!
• So S is exactly the same as the root-mean-square deviation (RMSD)?
• Sal says S is the 'typical error' or the standard deviation of the residuals, so I think you are correct?
(1 vote)
• Why is b equal to constant coefficient and m equal to caffeine coefficient? Can anyone please elaborate more?
• It's literally just how the computers calls the things it calculates.

We asked the computer to perform a least-squares regression analysis on some data with
x = caffeine consumed and y = hours studying

So imagine the data on a scatterplot, with caffeine consumed as the x-axis, and hours studying as the y-axis.

Now the computer calculates things and finds us a least-squares regression line. But, instead of just giving us the line in the form y = mx + b, it decides to put things into a weird table format.

First you have a column called "predictors", with "constant" and "caffeine" underneath. This is because with a least-squares line you can "predict" the value of y (hours studying) with

y = mx + b

where b is the "constant" that takes part in your prediction, and x is the caffeine. So b and x are the "predictors" of y.

Now the coefficient of x is m, and since x is the "caffiene" portion of your predictors, the coefficient of your caffeine predictor is m.

For b, you can imagine the equation as

y = mx + bx^0

And now, if you consider bx^0 as the "constant" predictor, the coefficient on it is b.

Ultimately, "constant coefficient" and "Caffeine coefficient" are just names the computer gave to m and b.
• What is the least amount of information you need to know to find the equation of a line?
(1 vote)
• To find the equation of the line, you need the slope and y-intercept. Solving for the slope just requires two points on the line that you're solving for.

Hope this helps!😄
• In this case, does the constant b, representing the y-intercept, show that the minimum number of hours spent studying was 2.544? Since our slope is positive, and when x=0 (minimum caffeine intake) that is the value of b?
(1 vote)
• I could be wrong, but I believe that 2.544 would represent the predicted minimum amount of hours spent studying as this is a best fit line, and not the exact value of every data point.
(1 vote)
• I'm confused because in the practice problems after the video, they use the same question but it says that the correct answer ŷ=2.544+0.164x. Is it because the order of numbers is different?
(1 vote)
• Yeah its just in a different order, the answer isn't different it was just written differently
(1 vote)
• Does correlation coefficient 'r' always equal to sqrt of coefficient of determination R2?
When I tried to derive the relation of r from relation of R2, I was not successful. please explain.
I don't think that r is sqrt of R2. Then, why in this video, it is mentioned like that?
(1 vote)
• If we have to have the x be certain dates like 1955 then 1961 how would we set the x's up to put them into the calculator?
(1 vote)
• None of the videos explain as to how we can figure out the slope and the intercept to achieve a least squares regression line without the help of the computer.
Please explain how to do it manually.
(1 vote)
• Positive slope means positive r. Negative slope means negative r. Just memorise that?