1. So far
--> looked at the effect of a discrete variable on a continuous variable
t-test, ANOVA, 2-way ANOVA

6. Often -
interested in the relationship between 2 or more continuous variables
REGRESSION
Eg height and age, height and weight, dose and response

7. Regression allows us to ask:
Is there a relationship between two variables?
If so, what is the form of the relationship?
How well does the form fit our data?
Can also be used to predict one variable based on the value of the other

8. Blood Pressure Decrease (mmHg)
Dose (mg)

9. Blood Pressure Decrease (mmHg)
Body Weight (kg)

10. BP Decrease (mmHg)
Body Weight (kg)
Dose (mg)

13. Weight (kg)
Intercept
Slope
Height (cm)

14. Weight (kg)
Height (cm)

15. Weight (kg)
Height (cm)

16. Weight (kg)
Height (cm)

17. Weight (kg)
Height (cm)

18. Weight (kg)
Height (cm)

19. Ordinary Least Squares - OLS
--> find the line that produces the
SMALLEST RESIDUAL SUM OF SQUARES

20. Residual Value
Weight (kg)
Height (cm)

21. Weight (kg)
Height (cm)

22. Weight (kg)
Height (cm)

23. Hypothesis Tests Regarding Regressionas

24. So, --> make inferences about the POPULATION
based on a sample.
Hypotheses:
Slope
Ho: 1 = 0
HA: 1  0
Intercept
Ho: 0 = 0
HA: 0  0
How do we assess these hypotheses?
Examine Sums of Squares!!

25. Weight (kg)
Height (cm)

26. Weight (kg)
Height (cm)

27. Weight (kg)
Height (cm)

28. ANOVA Table
Source of
Variation SS DF MS F 1
Regression
n-2
Residual
Total
n-1

29. How much of the variation in Y is explained by
the relationship?
--> Coefficient of Determination = r2 =
Weight (kg)
Height (cm)

31. Hypotheses:
Ho:  = 0
HA:   0

32. Scatter Plot of the Data

33. P << 0.05, therefore reject H0, there is a relationship
between fiber diameter and fiber strength.

34. Slope
Intercept

38. What is the predicted strength of a fiber that is
26um diameter?

49. Longevity = Bo + B1X1 + B2X2