Changing units in the simple ordinary least squares model Suppose you are studying how the birth weight of a child is affected by the smoking habits of the mother during pregnancy. After gathering data, you run a simple ordinary least squares (OLS) regression that yields the following results: bwght = birth weight of child in ounces cigs = average number of cigarettes smoked per day by the mother during pregnancy According to your regression results, if a mother smokes one more cigarette per day on average, the child's birth weight is predicted to ounces Suppose you would like to change the units of the dependent variable, bwght. Instead of measuring birth weight in ounces, you would like to measure birth weight in pounds. Let bwghtP represent the birth weight in pounds. Instead of rerunning your regression with bwghtP instead of bwght, you know you can calculate the new regression line by hand. The new regression line will be Suppose you decide not to change the units for birth weight (leaving it in ounces), but instead you would like to change the units of the independent variable, cigs. Instead of measuring smoking in terms of average cigarettes per day, you would like to measure smoking in terms of average number of packs per day. Let packs represent the average number of packs of cigarettes smoked by the mother per day during pregnancy. Instead of rerunning your regression with packs instead of cigs, you know you can calculate the new regression line by hand. Assuming each pack contains 20 cigarettes, the new regression line will be: