1. r = 0. 79 The correlation between price and calories is 0. 79
r = 0.79 The correlation between price and calories is This tells us there is a strong relationship, but it doesn’t tell us any of the details. For this we need to look at the line.

2. Linear Model: an equation that makes a straight line through data
b0 = y – b1x b1= r (sy/sx)
the equation: The equation of the line is found when the sum of squared residuals is the smallest The equation is wrong but useful in learning more about the world The equation summarizes a general pattern

3. How wrong is the model?

4. How to find the least square line (the linear model aka line of best fit)
Minimize the square of the residuals
square so -/+residuals do not cancel
square so heavier weight to large residuals

5. Use residuals to check if the model is correct
Residual on y axis
If a pattern in the residual graph something is wrong

6. Residuals show the amount of variation that is not explained by the model
R2 = fraction of variation accounted for by the model 1- R2 = fraction of variation in the residuals
r = 1 the model explains everything and no residuals
r = 0 then the model does not explain anything

7. Coefficient of Determination R2
The percentage of variance in one variable that is accounted for by the other variable

8. Example: Correlation between GPA and # hours you study: rGPA-Hours = 0

9. Correlation between GPA and # hours studying: rGPA-Hours = 0.7
Strong Relationship!!!
But exactly how strong?
The Coefficient of Determination can tell us
Coefficient Determination: r2 GPA-Hours = 0.49 Which means 49% of the variance in GPA can be explained by studying (and 51% is something else)

10. 49% of the change in GPA is due to studying
Find r
r = .7
2) Square r
.72 = .49
3) Turn into a percent
.49 * 100 = 49%
Write sentence:
49% of the change in GPA is due to studying
Find R2