Introduction to Scatter Plots and Relationships
Scatter Plot: A graph in the Cartesian plane which displays the joint distribution of two variables in which each point represents a pair of variable values.
Carnings E=10.25h+50
Independent variable
• a variable that affects the value of another variable
• Always placed on the horizontal axis
• can take any values
Dependent variable
• variable that is affected by some other variable (the independent variable)
• depends on the independent variable
• Always placed on the vertical axis
Outlier
• a point separated from the main body of data on a graph
Relationships/Correlations: We say that a Linear Correlation is:
Strong if the two variables vary at similar rates. Most of the points in the scatter plot will be quite close to a line of best fit. Visualize a tight oval.
Weak if the two variables vary at rates that are not similar. The scatter plot will have a visible pattern to it, but will be somewhat scattered. Think fat oval.
Positive if the slope of the line of best fit is positive. The two quantities increase together.
Negative if the slope of the line of best fit is negative. As x increases, y decreases.
If there is no trend or pattern, the points on the scatter plot will look completely random. Picture a square enclosing the points.
Example: Classify the following relationships/correlations.
Hypothesis
-an educated guess / prediction of an expected result
-a prediction of a possible relationship
Example 2:
a) Create a hypothesis about the relationship between the temperature in a town during the summer and the volume of water used by the town’s residents.
As the temperature increases, so does the volume of water used by the town`s residents.
b) What is the opposite of that hypothesis?
As the temperature increases, the volume of water used by the town`s residents decreases.
