Regression Worksheet

STA 3024, Spring, 2000

1. In a regression of y = salary on x = years of experience, the dummy variable D was coded 1 for males, 0 for females; the prediction equation was:

1. Assuming that all coefficients are significant, what is the prediction equation for males?

b) How much is the intercept for Females different from Males?

c) Sketch the prediction equations for Males and for Females

d) Suppose that -0.8 was not significantly different from zero. Interpret the fitted equation, using words from this particular problem, e.g. salary, females.

e) What does d) have to do with ANCOVA?

2. Suppose you have y = # species and x = % ground cover. You have data from three habitats, A, B, and C. Describe how you would set up a regression model

1. which allowed a linear relationship between y and x with different intercepts for each habitat. Code the dummy variables so that Habitat A is the reference habitat to which B and C are compared. Write out the model. How would you test whether Habitat B had a higher intercept than Habitat A?

b) which allowed a linear relationship between y and x with different intercepts and different slopes for each habitat. Build on the answer for part a). Write out the model. How would you test whether Habitat C had a different slope from Habitat A?

3. A fitted equation was

What is the fitted equation in terms of y? You can assume either natural or common logs.

How could you test whether y was proportional to x? Don't do the test, just describe it.