Question

Table 1: How to interpret logged models, table adapted from Bailey's textbook model equation Log-linear In Y; = Bo + BiX; + ei Linear-log Y; = Bo + B, In Xi + ei interpretation A one-unit increase in X is associated with a B1 percent change in Y (on a 0-1 scale). A one percent increase in X is associated with a B1/100 change in Y. A one-percent increase in X is associated with a B1 percent change in Y (on a 0-100 scale) Log-log In Yi = Bo + Bi In X; + ei Table 2: How to interpret logged models, Table adapted from Stock and Watson's textbook model equation In Y; = Bo + BiX; + ei Log-linear Linear-log Y; = Bo + Bi In Xi + ei interpretation A change in X by one unit (SX = 1) is associated with a 10031% change in Y. A one percent change in X is associated with a change in Y of 0.01ßı A one-percent increase in X is associated with a B1 percent change in Y, so B1 is the elasticity of Y with respect to X. Log-log In Y; = Bo + Bi In X; + ei

Answer 1

Q1

a) In colum on we see the results of regression equation where Weight is regressed on Doughnuts. It is a linear regression euqation. In this equation, if we say that weekly the consuption of dounts is increased by ! extra donut, then the weight of the person will increase by 9.224 pounds.

b) In column 2, Weight is regressed on Doughnuts and square of doughnuts. It is a plynomial regression. The weight on consumption of 5 doughnuts is- (5.143*5+0.221*(5^2)= 31.24) 31.24 pounds. In case of consumption of 6 doughnuts (5.143*6+0.221*(6^2)= 38.814) the weight is increased by (38.814-31.24) 7.574 pounts.

The weight on consumption of 19 doughnuts is- (5.143*19+0.221*(19^2)=177.498 ) 177.498 pounds. In case of consumption of 20 doughnuts (5.143*20+0.221*(20^2)= 209.824) the weight is increased by (209.824-177.498) 32.33 pounts.

c) In Table 1, under column 3, Weight is regressed on Log of Doughnuts. It is a linear log regression, thus if the consumption of doughnuts increase by 1% then the weight of the person increases by 0.52 pounds.

d) Column 4 shows the a log linear regression where Log of weight is regressed in Doughnuts. If the consumption of dounts increase by 1 dounut per week then the weight of the person increase by 4.9%.

Q2

a) In Column 2, Weight is the dependent variable and Female and Doughnuts are the independent variables. It shows the regression of Weights on Female dummy and Doughnuts. If the weekly consuption of doughnuts is increased by one-unit then the of the person increases by 8.670 pounds.

b) In Column 3, if the male doughnut consuption is scene, then the dummy variable of FEMALE and interaction variable of FEMALE*DOUGHNUT both will be zero. In such a case, one unit increase in the weekly consumption of dughnut by males will cause their weight to increase by 8.616 pounds.

However if there is a female who is taken into consideration, then if the consumption of doughnut is increased by one-unit per week then the weight is affected in the following manner- (-26.789+8.616+1.276= -16.897). It means that the weight if decreased by 16.9 pounds.