Friday, May 27, 2016

Daily Regents: Scatter Plot Residuals (August 2014)

I'll be reviewing a New York State Regents Exam Question every day from now until the Regents exams begin next month. At least, that is the plan.

August 2014, Questions 31

31. The table below represents the residuals for a line of best fit.
Plot these residuals on the set of axes below.
Using the plot, assess the fit of the line for these residuals and justify your answer.

Plot the points on the table. It should look like this:

If a regression line is a "good fit", the residuals should be scattered about, above and below the x-axis, randomly.
If a pattern emerges, then the regression is not a good fit for the data. (For example, suppose you did a linear regression, but the data suggested that you should have done a quadratic regression instead. Then a pattern will emerge in the residuals.)

The graph below shows that there is a pattern among the residuals, and it looks like it forms a curve.
DO NOT draw the curve! Just explain that it is not a good fit because of the pattern.

Any questions?

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