Question

Air Transporation model

Model Y = bo + b1* x1 + b2 * x2

For the 1st case, the Dependent variable is:- Revenue passenger per mile This variable is dependent on the independent variables like [ load factor and enplanements

For 2nd case, the Dependent variable is:- Load factor This variable is dependent on the two independent variables like [ available seats and enplanement ]

What is the model assumptions? Also how these models related to past economic theory on airline transportation or research?

Answer 1

a).

Consider the given regression model, which given by,

Y = b0 + b1*X1 + b2*X2, where all the coefficients are positive, Y and X2 be continuous variable and “X1” a dummy variable where “X1=1, for Female and 0 otherwise.

So, here “b0” be the intercept and “b2”, be the slope coefficient. So, if X1=1, => the given equation will be,   “Y = (b0+b1) + b2*X2” and if X1=0, then the given equation will be, “Y = b0 + b2*X2”.

So, consider the following fig, the estimated line for 2 quality of “X1”. So, we can see that if “X2=0”, then “Y” is more under “Female quality” compared to “Male” quality and if “X2” increase by “1” unit given the variable effecting “Y” remain same => “Y” will increase by “b2” unit irrespective of any quality, => here the dummy variable is “intercept dummy” which effect the “dependent variable” through intercept and totally independent of any other variable in the model

So, we can say the “Y” for female and male will be parallel to each other with same slope

b).

Now, consider the given model, Y = b0 + b1*X1*X2 + b2*X2, where “X1” be a dummy variable where “X1=1, for Female and 0 otherwise, and all the coefficients are positive.

So, if X1=1, => the given equation will be,   “Y = b0 + (b1+b2)*X2” and if X1=0, then the given equation will be, “Y = b0 + b2*X2”.

So, consider the following fig, the estimated line for 2 quality of “X1”. So, we can see that if “X2=0”, then “Y” is same or equal for both “Female” and “Male” quality and if “X2” increase by “1” unit given the variable effecting “Y” remain same => “Y” will increase by “b1+b2”, under “female” quality and “b2” for male quality, => here the dummy variable is “slope dummy” which effect the “dependent variable” through other independent variable. When “X2=0”, then “Y” is same and as “X2” increase the difference ion Y between 2 quality start increasing.

So, we can say the “Y” for female and male is not parallel to each other, they have same intercept with different slope.

c).

Now, consider the given model, Y = b0 + b1*X1 + b2*X2 + b3*X1*X2, where “X1” be a dummy variable where “X1=1, for Female and 0 otherwise, and all the coefficients are positive.

So, if X1=1, => the given equation will be,   “Y = (b0 + b1) + (b2+b3)*X2” and if X1=0, then the given equation will be, “Y = b0 + b2*X2”.

So, consider the following fig, the estimated line for 2 quality of “X1”. So, we can see that if “X2=0”, then “Y” is more under “Female quality” compared to “Male” quality and if “X2” increase by “1” unit given the variable effecting “Y” remain same => “Y” will increase by “b2+b3”, under “female” quality and “b2” for male quality, => here the dummy variable is “intercept dummy as well as slope dummy” which effect the “dependent variable” through intercept as well as through other independent variable. When “X2=0”, then “Y” is > for “female” quality and as “X2” increase the difference in Y between 2 quality is getting wider.

So, we can say the “Y” for female and male is not parallel to each other and they also have different intercept.