Econ 399 Chapter2b - 2.4 Units of Measurement and...

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Unformatted text preview: 2.4 Units of Measurement and Functional Form-Two important econometric issues are: 1) Changing measurement-When does scaling variables have an effect on OLS estimates?-When does scaling variables have no effect on OLS estimates? 2) Functional Forms-How do natural logs affect linear regressions?-How do functional forms impact elasticity? 2.4 Units of Measurement and Functional Form • Consider the following model:-where the number of squirrels and trees are in single units-if trees=2000 then the predicted number of squirrels becomes 1500-if there are no trees, there are 500 squirrels-how does this change if squirrels are measured in hundreds (ie: divided by 100)? (ie) 5 . 500 ˆ i i trees rrels i squ + = 2.4 Units of Measurement and Functional Form-If squirrels are measured in hundreds, then zero trees would produce 500 squirrels, so B hat=5 (divided by 100)-If there are 2,000 trees, then B 1 hat*2000 must equal 10 (15-5, or 1,000 squirrels)-Therefore B 1 hat=0.005 (divided by 100) (ie) 005 . 5 ˆ i i trees rrels i squ + = 2.4 Acorns are for the squirrels Therefore When the dependent variable is multiplied (divided) by a constant… Multiply (divide) the OLS intercept and slope by the same constant. IE: Change the y – change OLS the same way. 2.4 Units of Measurement and Functional Form • Consider the following model:-where the number of treehuggers and trees are in single units-if trees=800 then the predicted number of treehuggers becomes 900-if there are no trees, there are 500 treehuggers-how does this change if trees are measured in hundreds (ie: divided by 100)? (ie) 5 . 500 ˆ i i trees ggers u treeh + = 2.4 Units of Measurement and Functional Form-If trees are measured in hundreds, then zero trees would produce 500 treehuggers, so B hat=500 (nothing has changed)-If there are 800 trees, then trees=8 and 8(B 1 hat) must equal 400 (900-500)-Therefore B 1 hat=50 (multiplied by 100) (ie) 50 500 ˆ i i trees rrels i squ + = 2.4 Acorns are for the squirrels Therefore When the independent variable is multiplied (divided) by a constant… Divide (multiply) the OLS slope (not intercept) by the same constant. IE: Change the x – change OLS slope the opposite way. 2.4 Units of Measurement and Functional Form How does R (goodness of fit) change when a 2.4 Functional Form Thus far, we have focused on LINEAR relationships-Linear relationships don’t capture all of the possible interaction between variables-Linear relationships assume that the first x has the same impact on y as the last x-changing impacts can be captured through the use of NATURAL LOGARITHMS 2.4 Log-Lin Model2....
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This note was uploaded on 03/14/2009 for the course ECON ECON 399 taught by Professor Priemaza during the Spring '09 term at University of Alberta.

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Econ 399 Chapter2b - 2.4 Units of Measurement and...

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