1. EQ: How well does the line fit the data?
Analysis of LSRL
EQ: How well does the line fit the data?

2. What would you conclude based on the graph?
Data from
Barrels of Rum Sold
Ministers in Boston

3. Reasons for strong correlation
Lurking variables: Something in the background that affects both variables the same way.
For the historical data, as population increased the number of ministers increased as did the amount of alcohol being sold.

4. Shoe size vs. Height Determine if a linear model is a good idea.
8.5 66 9
68.5
67.5
9.5 70 10 72
10.5
71.5
69.5 11 73 12
73.5 74
12.5
Determine if a linear model is a good idea.
Create a scatterplot and examine the relationship.
DON’T FIND THE LSRL!!!!

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

6. Find the LSRL using summary statistics

7. Interpret all of the values
r : There is a strong positive linear relationship
a: when the shoe size is 0 the height
is predicted to be inches
b: for every 1 increase in shoe size
the height will increase by 1.87 inches

8. Coefficient of Determination
The percent of variation in the y values that is explained by the linear model with x.
Coefficient of determination = r2
where r is the correlation.

9. The coefficient of determination between shoe size and height is. 8575
The coefficient of determination between shoe size and height is What does this mean????
85.75% of the variation in heights is explained by the linear model with shoe size.

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

11. Residuals A residual is the difference between an observed
value of the response variable and the value
predicted
by the
LSRL

12. Predictions
Predict the height of a person with a shoe size of 8.5

13. Residual Actual Data: Residual: Observed - Predicted 66-67.25 =-1.25
8.5 shoe size and 66 inches for height
=-1.25

14. Create the LSRL

15. Calculate Residuals

16. Evaluate Residual Plot
A good residual plot has No patterns No outliers Balance between +’s and –’s

17. Bad Residual Plots

18. Example How are American female (30-39) heights and weights related?
Create a scatterplot and comment on the relationship
Determine the LSRL, r, and r2 and interpret the values.
Evaluate the model by analyzing the residuals.
Predict the weight for a 63 inch female.
Calculate the residual for a 63 inch female.
How confident are you in your prediction?