1. Section 6.1: Scatterplots and Correlation (Day 2)

2. Correlation
Describes the direction and strength of a straight-line relationship between two quantitative variables.
Curved relationships are not described by a correlation.
Represented by the variable r.
Range for correlation is -1 to +1.

3. Correlation
If the correlation value is exactly -1, it is a straight negative direction line, with all points on line.
If the correlation value is exactly +1, it is a straight positive direction line, with all points on line.
The closer the correlation value is to or +1, the stronger the correlation.
The closer the value is to 0, the weaker the correlation.

4. Correlation Examples

5. How to Calculate Correlation
Calculate the means for the x and y values (x bar and y bar).
Calculate the standard deviations for the x and y values (Sx and Sy).
Calculate the z-score for each x value and y value.
(x – x bar) / Sx
(y – y bar) / Sy
Correlation is the “average” of the products of these z-scores …

6. Formula for Correlation
Remember Σ means you add up the sum of all of the values that meet the criteria.

7. Facts about Correlation
r matches the sign of the slope (positive slope = positive r value, negative slope = negative r value)
Correlation does not change when the units of measurement change because z-scores are used (changing from meters to yards, for example).
Correlation is strongly affected by outliers (can change a high number to a low number).

8. Facts about Correlation
Correlation ignores distinction between explanatory and response variables (if you switched the position on the graph, you would still have the same correlation. If they were both increasing, now they are both decreasing—still a positive correlation; if one was positive, one was negative, still a negative correlation.)

9. Homework
Page , #10, 12
Page 356, #16
Page 359, #18

10. Group Activity #1
The number of convertibles sold at a car dealership in a month and the average monthly temperature (degrees Fahrenheit).
Draw the scatterplot, find the mean for x and y, find the standard deviation for x and y, find all z scores and find the value of r (correlation value). You can use the calculator to find the values of mean and standard deviation. Round all answers to 2 decimal places.
Convertibles sold (x) 3 6 5 7 8
Avg. Monthly temp. (y) 42 50 58 62 75 77