1. Linear Trends and Correlations
MDM 4U Lesson 2.1

2. Linear Trends
trend - a pattern of average behavior that occurs over time
line of best fit - a straight line graph that best represents a set of data
y-intercept
slope

3. Correlations The apparent relationship between two variables.
No Correlation
Weak Positive Correlation

4. Correlations Moderate Positive Linear Correlation
Strong Positive Linear Correlation

5. Strong Negative Linear Correlation
Correlations
A correlation is the apparent relation between two variables.
strong or weak
positive or negative
may be linear, or have some other shape
Strong Negative Linear Correlation

6. Measuring Strength of Correlations
Correlations can be strong or weak, but how do we measure how strong or how weak they are?
Look at the Correlation Coefficient (r). (thank you Karl Pearson for developing the formula!)
You can look at the residuals to get a picture
You can sum the squares of the residuals to get a measure (you want this to be small)

7. Correlation Coefficient (r) Formula
Where:
r is between -1 and +1
it is -1 for a perfect negative correlation
it is +1 for a perfect positive correlation
it is 0 when there is no correlation

8. Correlation coefficient-1 +1
-.33
+.33
+.66
-.66
negative
positive
weak
moderate
strong

9. Finding r In Excel The graph tells you r-squared.
You can take the square root of this to get the value of r, while the slope of graph will tell you the direction (positive or negative).
In Excel

10. An example of a quadratic:

11. Calculating the Correlation Coefficient by hand (it’s not that bad…really, I’m not lying to you….)
See page 164 of your textbook. Example 2.
We need to help the farmer.
Look at each part of the formula and let’s discuss it:

12. Create a table first: See the table on page 164 if you get stuck
Temperature (x)
Yield (y) x2 y2 xy 4
1.6 8
2.4 10
2.0 9
2.6 11
2.1 6
2.2
See the table on page 164 if you get stuck

13. Use each ∑ to help you use the formula:

14. Your conclusion for the farmer:
The correlation coefficient is 0.47 which indicates a moderate positive, correlation between crop yield and mean temperature.

15. Homework:
Page 168 #1, 2, 3(Excel), 5a (Excel), 5b(no Excel), 5cde, 6bc(no Excel), 10, 12 (Excel optional).
In your homework you are creating 2 graphs in Excel (and calculating the r2) and calculating r by hand twice. And doing a few random questions. That’s not too much to ask.
Do your homework. Ask for help.