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

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Presentation transcript:

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

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

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

Blood Pressure Decrease (mmHg) Dose (mg)

Blood Pressure Decrease (mmHg) Body Weight (kg)

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

Weight (kg) Intercept Slope Height (cm)

Weight (kg) Height (cm)

Weight (kg) Height (cm)

Weight (kg) Height (cm)

Weight (kg) Height (cm)

Weight (kg) Height (cm)

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

Residual Value Weight (kg) Height (cm)

Weight (kg) Height (cm)

Weight (kg) Height (cm)

Hypothesis Tests Regarding Regression as

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!!

Weight (kg) Height (cm)

Weight (kg) Height (cm)

Weight (kg) Height (cm)

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

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

Hypotheses: Ho:  = 0 HA:   0

Scatter Plot of the Data

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

Slope Intercept

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

Longevity = Bo + B1X1 + B2X2