1. Statistical Relationship Between Quantitative Variables

7. Statistical Relationship Between Quantitative Variables
Statistical relationship points to overall tendencies rather than strict rules (e.g., smoking – cancer).
Scatter plots
X – explanatory variable
Y – response variable
Interpreting scatter plots:
Form, Direction, Strength.

8. Statistical Relationship Between Quantitative Variables
The simplest form is the Linear Relationship
Math grade
Statistics Grade

9. More Complicated Forms of Statistical Relationships
Electricity shortage
Mean Monthly Temperature

10. No Relationship

11. Linear Relationship

12. B. Negative linear relationship
A. Positive linear relationship
C. Weak positive relationship
D. Strong negative relationship

13. Linear Correlation Coefficient
The linear correlation coefficient (r) is a measure for the direction and strength of a linear relationship between two quantitative random variables.

14. r(X,Y) – Basic Idea (Positive)
Y – income ($) Y
Average of Y X
Average of X
X – education (yrs)

15. r(X,Y) – Basic Idea (Negative)
Y – Statistics grade
Average of Y X
Average of X
X – Time in Pubs (hrs/week)

16. Linear Regression Line (predicting Y from X)
The ‘best’ line that fits the scatter plot is the one that minimizes the sum of the (square of the) deviations