 # Statistical Relationship Between Quantitative Variables

## Presentation on theme: "Statistical Relationship Between Quantitative Variables"— Presentation transcript:

Statistical Relationship Between Quantitative Variables

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.

Statistical Relationship Between Quantitative Variables

More Complicated Forms of Statistical Relationships
Electricity shortage Mean Monthly Temperature

No Relationship

Linear Relationship

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

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.

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

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

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