Correlation The apparent relation between two variables Trend

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/math 9/strand 4/scatter. Plot. 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, r 2 • A number from 0 to +1 that gives the relative strength of the relationship between two variables. • If r 2 = 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 r 2 and explain what it means.

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

To do: Make a scatter plot using Open Calc for the data below x -4 -3 0 5 15 19 21 28 36 y 8 5 12 15 27 30 32 38 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, FINISH

To do: Make a line of best fit using Open Calc for the data below 1. Highlight the x -4 -3 0 5 15 19 21 28 36 y 8 5 12 15 27 30 32 38 50 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 R 2 7. What does R 2 tell you about the correlation

To do: Make a scatter plot using Open Calc for the data below x -4 -2 0 2 4 6 8 10 12 y 8 10 12 14 17 18 20 21 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, FINISH

To do: Make a scatter plot using Open Calc for the data below x -4 -2 0 2 4 6 8 10 12 y 8 10 12 14 17 18 20 21 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 R 2 7. What does R 2 tell you about the correlation

Compare Graph 1 and 2 • Which one of your two graphs show stronger correlation? How can you tell? ? ?