Answer:
Step-by-step explanation:
a. How many dummy variables are needed to represent the categorical variable?
We need 1 less dummy variable than outcomes for the categorical variable.
categorical variable has 2 outcomes
So, we need 2-1 = 1 dummy variable.
Answer: 1
Note: If our categorical variable had 5 outcomes, we would need 5-1 = 4 dummy variables.
b. Write the multiple regression equation relating the dependent variable to the independent variables.
Note: Depending your your professor, this can be written one of the following ways...
yhat = a + b1 x1 + bx2
yhat = b0 + b1 x1 + b2 x2
yhat = beta0hat + beta1hat x1 + betahat2 x2
where x1 is the ratio variable
and x2 is the dummy variable
c. Interpret the meaning of the coefficients in the regression equation.
b0 = the predicted value of y when x1 and x2 both equal 0.
b1 = the change in y when x1 increases by 1 unit holding x2 constant.
b2 = the predicted difference in y between the two possible outcomes of the categorical variable holding x1 constant.
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