1. Chapter 3: Linear models
EQ: How can bivariate data be analyzed?

2. Scatter Plots can SAVE lives
The forecasted temperature for January 20, 1986 was 31 degrees.

3. Scatterplots Shows the relationship between 2 quantitative variables.
X: explanatory variable
Y: response variable

4. Analysis Look at the overall form and any deviations
Form: Linear or not linear and does the
Data have any Clusters, outliers, or
patterns
Direction: Positive or negative association
Strength: weak, moderate, strong

5. Examples Explanatory Variable Number of bikes Response Variable
Number of accidents
Form:
Linear. Possible outlier
Direction:
Positive association
Strength
Strong

6. Examples Explanatory Variable Time swimming Response Variable
Pulse rate
Form:
Linear. Scatter seems to increase as the time increases
Direction:
Negative association
Strength
moderate

7. Examples Explanatory Variable Percent without HS diploma
Response Variable
Teacher Pay
Form:
Large cluster of data between 10 and 30 %.
Direction:
none
Strength
weak

8. Example Effects of Humor on Test Anxiety and Performance Anxiety Score23 43 14 59 48 77 7 50 20 52 46 15 51 21
Construct a scatterplot of anxiety vs. exam score. Describe the strength, direction, and form.

9. Correlation Definition: The strength of the linear relationship
Notation:
Correlation = r
Values
-1 < r < 1
Interpretation
The closer r is to 1 or -1 indicates a stronger linear relationship
A correlation near 0 indicates no linear relationship
Cautions:
Look at the data first and make sure a linear relationship is feasible

10. Examples

11. Line of best fit Method: Minimize the sum of the squared errors
Prediction line
Predicted value
Error
Actual value

12. LSRL Equation
Y-intercept
Y-hat
Slope

13. Facts about the LSRL Line
Every LSRL line passes through
All found in 2 variable stats

14. Interpretations Slope:
For every 1 unit increase in x, the y changes by the slope
Intercept:
When x is 0, y is a.
May not have any PRACTICAL meaning

15. Dinosaur Bones
Archeologists want to determine if a new bone belongs to a certain species of dinosaur. They have a set of bones that they KNOW go together and have recorded the Femur lengths and Humerus lengths. Analyze the data and determine if there is a relationship.
Create a scatterplot
Analyze the scatterplot
Find the correlation
Find the LSRL
Interpret
Femur
Humerus 38 41 56 63 59 70 64 72 74 84