1. Simple Linear Regression
Section 13.1

2. Deterministic Relationship
If the value of y (dependent) is completely determined by the value of x (Independent variable)
Most are not determined completely by another

3. Probabilistic Model
Description of the relation between 2 variables that are not deterministic.
It allows y to be larger or smaller than f(x) by a random amount, e.
Y = f(x) +e

4. Let x* denote the value of x….

5. Simple Linear Regression Model
Assumptions about the distribution of e
Mean
St. Dev.
Distribution of e at any x value is normal
Random deviations associated with different observations are independent of 1 another

6. Slope Average change in y associated with a 1 unit increase in x.
Point estimate is b.
Y-intercept’s point estimate is a.

7. X* denotes a specified value of the predictor variable x ….
So has 2 different interpretations
It is a point estimate of the true mean y value when x = x*.
It is a point predictor of an individual y value that would be observed when x = x*.

8. Find the point estimate of the mean y-value for the following:
Age (x) 15 17 18 16 19 20
Weight (y)
2289
3393
3271
2648
2897
3327
2970
2535
3138
3573
So what’s the point estimate for an 18 year old mom?

9. Point estimate and point prediction are identical – only the interpretation is different.
Prediction – weight of single baby who mom is 18
Estimate – average weight of all babies born to 18 year-olds

10. Answer the following: Explain the slope in context of the problem
Explain the y-intercept in context of the problem.

11. Find SSResid.
on calculator – every time you calculate a linear regression – it calculates the residuals. Put them in list 3 and square them & add the list.

12. Point estimate of is
It represents the typical deviation in the y-variable from the least squares line.

13. Find the residual for a mother who is 19.

14. Find the probability that a 19 year old mother has a baby that is more than 3000 g.

15. Coefficient of determination (r2)
It’s the amount of variation in the y-variables that can be explained by the least squares line.

16. Homework
Worksheet