1. Critical Analysis

2. b) Do a regression on this data to calculate the line of best fit
The following data represents 5 students from a class of 20.
Create a scatter plot to model the following data.
b) Do a regression on this data to calculate the line of best fit
c) Calculate the correlation coefficient
d) Does your model seem appropriate?
Height (cm)
Grade
161 49
170 66
182 73
199 87
189 88

3. The rest of the class data is as follows The scatter plot for this data would look like this:
Height
Grade
162 65
170 66
155 82
158 88
160 81
161 49
182 87
189 73
192 52
199
151
153 74
168 56
177 46
178 45
164 41
169 85
175 54
Notice the correlation coefficient is only

4. What went wrong? The sample size was too small
A sample size which is too small can lead to predictions using the model to be invalid

5. The following data shows the average salary in the NHL since 2000.
Year
Salary
2000
$1,356,380
2001
$1,434,885
2002
$1,642,590
2003
$1,790,209
2004
$1,830,126
2005
1,830,126
2006
$1,460,000
2007
$1,708,607
2008
$1,906,793
2009
$2,126,843
a) Create a scatter plot to model this data
b) Do a regression on this data to calculate the line of best fit
c) Calculate the correlation coefficient
d) Does your model seem appropriate?

6. Notice the correlation coefficient is only 0.5391

7. Notice what happens when we spilt the data up and create a scatter plot for the years and separately.
The correlation coefficients are quite high for both these graphs.
Why did this happen?
In 2005 there was a league wide lockout and a salary cap was introduced bringing all salaries down. After this year salaries continued to rise again.
This is an example of a hidden variable

8. Questions to ask when performing critical analysis
Is the sampling free of bias?
Could outliers influence the results?
Are there unusual patterns which suggest a hidden variable?
Has causality been inferred with only correlation evidence?

9. Homework/Practice
p #1-3,5,6,8