2 nd Day: Bear Example. Residual = observed y – predicted y. A residual plot plots the residuals on the vertical axis against the explanatory variable on the horizontal axis. The plot magnifies residuals and makes patterns easier to see. The mean of the residuals is always zero.
Enter data from table, p. 234
Find vital stats
Find residuals for data
x 0 3 6
y 0 10 2
Association between x and y: positive, but weak
= 4. The total area of these 3 squares is a measure of the total sample variability.
0 0 16
3 10 36
6 2 4
= (3, 4) (always the case)
0 0 9
3 10 36
6 2 9
is the proportion of the total sample variability that is explained by the least-squares regression of y on x.
Strong positive linear association. The correlation is r = .9749. Since r-sq = .9504, the regression of of y on x will explain 95% of the variation in the values of y.
The AP Statistics exam was first administered in May 1997 to the largest first-year group in any discipline in the AP program. Since that time, the number of students taking the exam has grown at an impressive rate. Here are the actual data. Begin by entering them into your calculator lists.
Year # students
1. Use your calculator to construct a scatterplot of these data using 1997 as Year 1, 1998 as Year 2, etc. Describe what you see.
2. Find the equation of the least-squares line on your calculator. Record the equation below. Be sure to define any variables used.
3. Interpret the slope of the least-squares line in context.
4. How many students would you predict took the AP Statistics exam in 2006? Show your method.
5. Construct a residual plot. Sketch it in the space below. Comment on what the residual plot tells you about the quality of your linear model.
6. Interpret the value of from your calculator in the context of this problem.