x
y
2
3
5
6
7
9
10
1
4
6
5
9
8
11
yˆ
y  yˆ
11
10
9
8
7
6
5
4
3
2
1
1. Plot the scatterplot for the points above.
1
2 3
4
5 6
7
8 9 10 11
2. Find the LSRL and correlation coefficient. (Round to 4 decimal places)
yˆ = ______________________________
r = _________________
3. Use the LSRL to calculate the predicted (fitted) value for each x-value. Fill in the chart above.
4. Calculate the residuals ( y  yˆ )
and fill in the chart above.
6. Create another residual plot by plotting
the yˆ -values on the horizontal axis and the
vertical axis.
residuals on the vertical axis.
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
-1
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2
-1.4
-1.6
1
2
3
4
5
6
7
8
9 10 11
x
Residuals
x-values on the horizontal axis and the residuals on the
Residuals
5. Create a residual plot by plotting a scatterplot of the
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
-1
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2
-1.4
-1.6
7. What do you notice about these two residual plots?
8. Is the LSRL from question 2 an appropriate model for this data? Explain
1
2
3
4
5
6
7
8
9 10 11
9. Sketch a scatterplot of this data and calculate the LSRL.
Plot the LSRL on your scatterplot.
yˆ = ______________________________
10. Does there appear to be an influential point? IF so, which one?
Range of Motion
One measure of the success of knee surgery is post-surgical range of motion for the knee joint following a knee
dislocation.
Age
45
40
31
28
26
16
14
20
21
Range of Motion
205
137
133
122
135
135
108
120
127
Age
yˆ = ______________________________ r = _____
r2 = ______
12. Would you consider this point influential? Explain.
13. Write interpretations, in context, for the slope, r & r 2 for question 11.
Range of Motion
11. Remove the point from your list. Sketch a scatterplot of this
data and calculate the LSRL. Plot the LSRL on your scatterplot.
Age
14. Which of these measures would be considered resistant? (LSRL, correlation coefficient (r), or coefficient of
determination (r2))