Correlation

The apparent relation between two variables.

Trend

• A pattern of average behaviour that occurs over time

Which of the scatter plots indicate the strongest trends?

Which of the scatter plots do not indicate a trend?

If a line of best fit were drawn on each of the scatter plots that show a trend,

describe the slope of each line.

Which do you think show strong positive correlation and which shows

strong negative correlation?

Make your own scatter plot and examine the trends

• http://staff.argyll.epsb.ca/jreed/math9/strand4/scatterPlot.htm

Correlation Coefficient , r

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

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.

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.

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.

Example

• r=.9• This means there is a strong positive

correlation.

• Calculate r2 and explain what it means.

Residual PlotResidual Value – the vertical distance between a data point and the line of best fit

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

x y-4 8-3 50 125 1515 2719 3021 3228 3836 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

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

x y-4 8-3 50 125 1515 2719 3021 3228 3836 50

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

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

x y-4 8-2 100 122 144 176 188 2010 2112 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

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

x y-4 8-2 100 122 144 176 188 2010 2112 24

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

Compare Graph 1 and 2• Which one of your two graphs show stronger

correlation? How can you tell???