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## AP®︎/College Statistics

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

Lesson 4: Least-squares regression

# Using least squares regression output

Worked example using least squares regression output.

## Want to join the conversation?

• What are SE Coef, T, and P?
• Why is it called "least squares regression output?"
• Regarding regression, the term doesn't have anything to do with what it really does...
Extracted from this nice article from http://blog.minitab.com/blog/statistics-and-quality-data-analysis/so-why-is-it-called-regression-anyway:

"... here’s the irony: The term regression, as Galton used it, didn't refer to the statistical procedure he used to determine the fit lines for the plotted data points. (...) For Galton, “regression” referred only to the tendency of extreme data values to "revert" to the overall mean value. (...)
Later, as he and other statisticians built on the methodology to quantify correlation relationships and to fit lines to data values, the term “regression” become associated with the statistical analysis that we now call regression. But it was just by chance that Galton's original results using a fit line happened to show a regression of heights. If his study had showed increasing deviance of childrens' heights from the average compared to their parents, perhaps we'd be calling it "progression" instead.

So, you see, there’s nothing particularly “regressive” about a regression analysis."
• at , why does slope = fertility coef? and y-intercept = constant coef?
• To predict life expectancy (Yhat) based on fertility rate(X), it means for every 1 fertility rate change (delta X = 1) you want to know how much does the life expectancy changes (delta Y). Hence, you use the slope (delta Y/ delta X) to be the coefficient of fertility. When you multiply the fertility rate given by this coefficient then you know Y (life expectancy) would change by how much.

For y-intercept as a constant coefficient I think it's because this is the point in the graph where you know for certain that the linear regression line will pass through, hence the name constant. This value could very well be the mean value of y because every linear regression line will pass through the mean of x and y (x,y) coord. Hopefully, somebody passing by would confirm or correct me on this if my understanding is wrong.
• What software gives this output?
What do the other entries in the table represent?
• Life expectancy of whom?

The mothers, the children, or the population as a whole?