http://www.ck12.org Chapter 9. Regression and Correlation- When there is anonlinearrelationship, we are able totransformthe data usinglogarithmic and power
transformations. Since logarithms and power transformations are exponential in nature, this allows us to
produce a linear relationship to which we can fit a regression line. - The difference between the actual and the predicted values is called theresidual value. We can calculate
scatterplots of these residual values to examineoutliersand test forlinearity.
Review Questions
The school nurse is interested in predicting scores on a memory test from the number of times that a student exercises
per week. Below are her observations:TABLE9.11: A table of memory test scores compared to the number of times a student exercises
per week.
Student Exercise Per Week Memory Test Score
1 0 15
2 2 3
3 2 12
4 1 11
5 3 5
6 1 8
7 2 15
8 0 13
9 3 2
10 3 4
11 4 2
12 1 8
13 1 10
14 1 12
15 2 8- Please plot this data on a scatterplot (Xaxis – Exercise per week;Yaxis – Social Events).
- Does this appear to be a linear relationship? Why or why not?
- What regression equation would you use to construct a linear regression model?
- What is the regression coefficient in this linear regression model and what does this mean in words?
- Calculate the regression equation for these data.
- Draw the regression line on the scatterplot.
- What is the predicted memory test score of a student that exercises 3 times per week?
- Do you think that a data transformation is necessary in order to build an accurate linear regression model?
Why or why not? - Please calculate the residuals for each of the observations and plot these residuals on a scatterplot.
- Examine this scatterplot of the residuals. Is a transformation of the data necessary? Why or why not?
Review Answers
- Answer to the discretion of the teacher.
- Yes. When plotted, the data appear to be negatively correlated and in a linear pattern.