There is quarterly information from 2010 to 2013 about the FlyingHigh (FH) airline.
This data is reported in the following table:
|
Year
|
Quarter
|
QD
|
PFH
|
PR
|
M
|
|
2010
|
Q1
|
64.8
|
250
|
250
|
104
|
|
|
Q2
|
33.6
|
265
|
250
|
101.5
|
|
|
Q3
|
37.8
|
265
|
240
|
103
|
|
|
Q4
|
83.3
|
240
|
240
|
105
|
|
2011
|
Q1
|
111.7
|
230
|
240
|
100
|
|
|
Q2
|
137.5
|
225
|
260
|
96.5
|
|
|
Q3
|
109.6
|
225
|
250
|
93.3
|
|
|
Q4
|
96.8
|
220
|
240
|
95
|
|
2012
|
Q1
|
59.5
|
230
|
240
|
97
|
|
|
Q2
|
83.2
|
235
|
250
|
99
|
|
|
Q3
|
90.5
|
245
|
250
|
102.5
|
|
|
Q4
|
105.5
|
240
|
240
|
105
|
|
2013
|
Q1
|
75.7
|
250
|
220
|
108.5
|
|
|
Q2
|
91.6
|
240
|
230
|
108.5
|
|
|
Q3
|
112.7
|
240
|
250
|
108
|
|
|
Q4
|
102.2
|
235
|
240
|
109
|
Where: QD is the average number of seats in economy class in FH; PFH is the average price (in US dollars) of the seat in economy class of FH; PR is the average price (in US Dollars) of the seat in the economic class of the competitor closest; and, M is the income level (in thousands of American dollars) of the region where FH operates and its main competitor.
According to this:
1- Show the correlations between QD, PFH, PR, and, M. Relief the signs of the correlations that has QD with the rest of variables.
According to economic theory have, Did you sense these signs?
|
correlations
|
QD
|
PFH
|
PR
|
M
|
|
QD
|
1
|
-0.76558
|
0.227258
|
-0.11685
|
|
PFH
|
|
1
|
-0.15292
|
0.506505
|
|
PR
|
|
|
1
|
-0.49197
|
|
M
|
|
|
|
1
|
Now the correlation of PFH is negative with QD because more the seats , less will be the price, negative of PR and PFH , because if the PFH has high price competitor will keep it low so opposite correlation. M is positive with PFH , because if income is high he will be ready to pay high for seats.
Convert the data into logarithms and run the following specification:
Ln(QD)t = a + b * Ln(PFH)t + c * Ln(PR)t + d * Ln(M)t + errort
Expected signs b <0 by the demand law and c> 0. a is the intercept, and, t: 1,2,3, ...., 16.
2-With Minimum Ordinary Squares (MCO), using Excel (Data Analysis Regression), run the regression of the previous specification and show the estimates of a, b, c, y,d. Present a summary of your "outcome"
2- Indicate if the estimates have the expected signs. Use the definitions of elasticities
Negative sign with log PFH is nice because more seats means less price, log PR is positive because if the competitor is increasing the price , then in order to lower the price one has to increase seats , income is positive because if people are ready to pay more , then more benefit from high no of seats.
3- Indicate if the estimates are statistically significant at 0.1%, 1%, 5% or 10%.
4- df. 1.345 1.761 2.145 2.624 2.977 3.787
5- ν 0.90 0.95 0.975 0.99 0.995 0.999
so when we see the log PFH , it Is not significant at any level, log PR is significant at 10 & 5% , log M is significant at all level.
6- Interpret the coefficient of determination (R-squared) and the test F.
R square is high because the model is good, F test is significant because all the variables are not zero.
7- How does QD change, if PFH goes up by 10%? Is FH an inelastic good? Explain
Is it a good decision to raise the price?
The PFH variable is not significant, so we won't see its impact on QD change
7- How does QD change, if PR drops by 11%?
If PR drops by 11 % , the QD will drop by more than 22 %
8- How does QD change, if M goes up by 5%?
If M goes up by 5 % QD goes up by more than 23 %