Correlation

1
Correlation

• The apparent relation between two variables.

2
Trend

• A pattern of average behaviour that occurs over
  time

3
Which of the scatter plots indicate the strongest
trends?
4
Which of the scatter plots do not indicate a
trend?
5
If a line of best fit were drawn on each of the
scatter plots that show a trend, describe the
slope of each line.
6
Which do you think show strong positive
correlation and which shows strong negative
correlation?
7
Make your own scatter plot and examine the trends

• http//staff.argyll.epsb.ca/jreed/math9/strand4/sc
  atterPlot.htm

8
Correlation Coefficient , r

• A number from 1 to -1 that gives the strength
  and direction of the relationship between two
  variables.

9
Positive Correlation

• If there is a positive correlation, the
  coefficient is a number between 0 and 1.  If
  there is no relationship between the predicted
  values and the actual values the correlation
  coefficient is 0 or very low (the predicted
  values are no better than random numbers).  As
  the strength of the relationship between the
  predicted values and actual values increases so
  does the correlation coefficient.  A perfect fit
  gives a coefficient of 1.0.  Thus the higher the
  correlation coefficient the better.

10
Negative Correlation

• If there is a negative correlation, the
  coefficient is a number between 0 and -1.  If
  there is no relationship between the predicted
  values and the actual values the correlation
  coefficient is 0 or very low (the predicted
  values are no better than random numbers).  As
  the strength of the relationship between the
  predicted values and actual values increases so
  does the correlation coefficient.  A perfect fit
  gives a coefficient of -1.0.  Thus the
  higher the correlation coefficient the better.

11
(No Transcript)
12
Coefficient of Determination, r2

• A number from 0 to 1 that gives the relative
  strength of the relationship between two
  variables.
• If r2 0.44, this means 44 of the variation of
  the dependent variable is due to variation in the
  independent variable.

13
Example

• r.9
• This means there is a strong positive
  correlation.
• Calculate r2 and explain what it means.

14
Residual Plot
Residual Value the vertical distance between a
data point and the line of best fit
15
To do Make a scatter plot using Open Calc for
the data below
x y
-4 8
-3 5
0 12
5 15
15 27
19 30
21 32
28 38
36 50

1. Enter data for x vertically in Column 1
2. Enter data for y vertically in Column 2
3. Highlight data and click INSERT and then CHART
4. Select XY(Scatter) to get a scatter plot
5. Click, NEXT, NEXT, FINISH

16
To do Make a line of best fit using Open Calc
for the data below

1. Highlight the graph
2. Click INSERT, TREND LINE
3. Choose LINEAR
4. Click SHOW EQUATION and SHOW COEFFICENT before
   pressing OK
5. What is the equation?
6. What is R2
7. What does R2 tell you about the correlation

x y
-4 8
-3 5
0 12
5 15
15 27
19 30
21 32
28 38
36 50
17
To do Make a scatter plot using Open Calc for
the data below
x y
-4 8
-2 10
0 12
2 14
4 17
6 18
8 20
10 21
12 24

1. Enter data for x vertically in Column 1
2. Enter data for y vertically in Column 2
3. Highlight data and click INSERT and then CHART
4. Select XY(Scatter) to get a scatter plot
5. Click, NEXT, NEXT, FINISH

18
To do Make a scatter plot using Open Calc for
the data below

1. Highlight the graph
2. Click INSERT, TREND LINE
3. Choose LINEAR
4. Click SHOW EQUATION and SHOW COEFFICENT before
   pressing OK
5. What is the equation?
6. What is R2
7. What does R2 tell you about the correlation

x y
-4 8
-2 10
0 12
2 14
4 17
6 18
8 20
10 21
12 24
19
Compare Graph 1 and 2

• Which one of your two graphs show stronger
  correlation? How can you tell???