The group indicator is set to xi = 0 for one group and xi= 1 for the other group. Suppose we used as the group indicator xi* = −1 for the first group and xi* = +1 for the second group. How will this change the estimates of β0 and β1 and the meaning of the test that β1= 0?
(Data file: cathedral) The data file contains the Height and Length in feet of 25 cathedrals, nine in the Romanesque style, and 16 in the later Gothic style. Consider only the first 18 rows of this data file, which contain all the Romanesque cathedrals and nine of the Gothic cathedrals, and consider testing the hypothesis that the mean length is the same for Romanesque and Gothic cathedrals against the alterative that they are different. Use these data to verify all the results of the preceding sections of this problem. (Hint: In the data file the group indicator Type is a text variable with values Romanesque and Gothic that you may need to convert to zeros and ones. In R, for example, the statement
will do it. Don’t forget to remove the last seven rows of the file, although if you do forget the test computed will still be a t-test of the hypothesis that the two types of cathedrals have the same mean height, but based on different data.)
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