An archive of Mark's Fall 2017 Intro Stat course.

# The regression problem handout

audrey

I’m having trouble with this regression problem we’re supposed to know for the final exam - particularly, finding the formula for the regression line. Any help would be appreciated!

The figure below shows a scatter plot of weight (in pounds) vs height (in inches) for a random sample 40 American men and the table shows linear regression table for that same data. We are curious if there is a relationship between height and weight.

a) Write down the hypothesis statement that we would check with this linear model.
b) Write out the formula for linear model.
c) What does the model predict for the weight of a man who is 70 inches tall?
d) State the conclusion of the hypothesis test from part ( c ).

mark

The regression line has the form

y=mx+b

or, since we want weight W as a function of height H ,
W=mH+b.

The part that we need to focus on in in the regression output is here:

This says that the coefficient of H is 5.7984 and the intercept ( b ) is -226.9576 . Thus, our model is

W = 5.7984H - 226.9576.

For example, the model predicts that a person who is 70 inches tall should weigh
5.7984\times70 - 226.9576 = 178.9304.