Here is a link to a data set that consists of a subset of the BMI data we have been using in class. The three columns of data are:
For the third variable, a value of 1 indicates that the entire family attends church regularly. A value of 2 indicates that there is some church attendance in the family, but it is sporadic or involves only some of the family members. A value of 3 indicates that no one in the family attends church.
Your task is to use the methods demonstrated in class on March 1 and March 3 to assess whether the regression of BMI on income differs depending on church attendance.
Regardless of what you concluded in Part One, imagine that you are planning to replicate the same investigation with a new sample. You have a theory that strongly suggests that the slope of the regression of BMI on income should vary depending on church attendance. Assume that the change in R-squared that you observed in Part One when you dropped the variables representing the interaction between church attendance and income is a good estimate of the true change in R-squared. Conduct a power analysis to determine how large a sample you would need in order to have power of .80 to detect that change in R-squared. (Assume an alpha level of .05.)