2. WELCOME BACK EVERY ONE! Hope you had a nice vacation! Hope you had a nice vacation!

3. Back already! This week… Mon- 13.1 and 13.2 notes and packet. Tues – 13.6 notes and class work. Wed- Review 13.6 homework and more examples. Thurs- Quiz on 13.6 Fri – Euler’s Circuits and Paths worksheet. Start Looking at Projects.

4. 13.1 and 13.2 Simple Linear Regression- Should be familiar stuff.

5. Linear Regression Linear Regression- equation that gives a straight line between two variables. y = A + B * x Gives EXACT relationship. Where A is the Y-INTERCEPT (initial value) And B is the SLOPE (how much y changes for each 1 unit of x).

6. Definitions X is the ____________ variable. Y is the ____________ variable. Linear -Exact- Nonlinear

7. Most relationships between x and y are NOT exact y = A + B * x + is a Greek Epsilon. It stands for Random Error. A and B are Population parameters.

8. y = A + B * x +

9. Called the Probabilistic Model y = A + B * x + represents: –1.) Missing or omitted variables Ex: If x is income and y is food expenditure. Maybe x (income) is not the only variable controlling y (food expenditure). Another variable may be family size. –2.) Random Variation Ex: Human variation. Maybe you spend more money on food one month (holidays) as opposed to others.

10. 13.6 part 1 Linear Correlation Linear Correlation Coefficient- ( or r ) measures the strength of the linear association between 2 variables. Tells How close the points are spread around the regression line. Notation:

11. When r = 1, we have a perfect Positive Linear Correlation

12. When r = -1 we have a perfect Negative Linear Correlation

13. When r = 0, we have NO Linear Correlation

14. Regression Packet From a scatter plot you can find the best fit (regression line). We will do so using our TI – 84 plus calculators. Follow packet instructions to calculate regression lines and predict other values not in chart as well as r values. Turn in when finished.

15. 13.6 part 2 Hypothesis Testing We will test Linear Correlation Coefficient- ( or r ) - measures the strength of the linear association between 2 variables (How close points are to regression line). Notation:

16. Hypothesis Testing for p Step 1: State HypothesisExample: –We will always use 0 for H 0 and H 1. Step 2: Given significance level in problem, find your Critical rejection t values and draw picture. –Use t chart were area in right tail is alpha. –Also for these tests we use df = n – 2.

17. Hypothesis Testing Step 3: Calculate r value for data using calculator. Step 4: Using this r value and the following formula to find the test statistic t. Step 5: Make a decision- Compare critical values from step 2 and test statistic from step 4.

18. Different Hypotheses Testing claim that there is a significant linear correlation (Two tailed). Testing claim of Negative Correlation (Left- tailed). Testing claim of Positive Correlation (Right- tailed).

19. Example- Testing linear correlation Using the following data test at the 1% significance level whether the linear correlation coefficient between the incomes and food expenditures is positive. Income (thous.) 35492139152825 Food (hund.) 915711589

20. Solution Step 1: State Hypothesis Step 2: Find Critical rejection t values and draw picture. –Area in right tail is alpha =.01. (Don’t have to cut in half since not two tailed). –Also for these tests we use df = n – 2= 7 – 2 = 5. Using this in chart we get: t = 3.365

21. Hypothesis Testing Step 3: Calculate r value for data using calculator. –You should get r =.96. Step 4: Using this r value and the following formula to find the test statistic t.

22. Conclusion Step 5: Make a decision- Since t = 7.667 our test statistic is greater than the critical value we got from the table t = 3.365, we REJECT H 0 ! There is a positive linear relationship between incomes and food expenditures.

23. Homework Page 615 (66, 75 c d, 76, 77) Review and quiz on 13.6 tomorrow. So I’ll do 75 with you to get you started.