You are hired to help this company determine an optimal strategy. You initially
ID: 1192948 • Letter: Y
Question
You are hired to help this company determine an optimal strategy. You initially collect data on competitor's price and income for your analysis. [The income data are from an index of economic performance in the market segments where the airline operates.]
Period
Q
P
Pc
Y
2011.Q1
64.8
250
250
104
2011.Q2
33.6
265
250
101.5
2011.Q3
37.8
265
240
103
2011.Q4
83.3
240
240
105
2012.Q1
111.7
230
240
100
2012.Q2
137.5
225
260
96.5
2012.Q3
109.5
225
250
93.3
2012.Q4
96.8
220
240
95
2013.Q1
59.5
230
240
97
2013.Q2
83.2
235
250
99
2013.Q3
90.5
245
250
102.5
2013.Q4
105.5
240
240
105
2014.Q1
75.7
250
220
108.5
2014.Q2
91.6
240
230
108.5
2014.Q3
112.7
240
250
108
2014.Q4
102.2
235
240
109
Since the company was in the habit of using only internal data to determine its demand curve,
bivariate analysis of the internal data using the OLS regression technique yielded:
Model 1.
Qd =
478.5
- 1.63 P
(5.44)
(-4.45)
R-squared =
0.58
F-statistic =
19.8
Adjusted R-squared =
0.56
S.E. of regression =
18.6
Variables =>
Constant
P
Coefficients =>
478
-1.63
Values =>
240
Q = 87
478
-391
NOTE: The numbers in parentheses (x.yz) under the coefficient estimates are "t statistics."
Utilizing the "outside information” that you collected, you re-estimated the demand equation using two alternative models:
Model 2.
Qd = 388.86 - 1.59 P + 0.3333 Pc
(2.32) (-4.21) (0.63)
R-squared = 0.60 F-statistic = 9.7
Adjusted R-squared = 0.54 S.E. of regression = 19.0
Variables =>
Constant
P
Pc
Coefficients =>
390
-1.6
0.3333
Values =>
240
243
Q = 87
390
-384
81
Model 3.
Qd =
28.844
- 2.1235 P
+ 1.035 Pc
+ 3.089Y
(0.17)
(-6.24)
(2.22)
(3.09)
R-squared =
0.78
F-statistic =
13. 9
Adjusted R-squared =
0.72
S.E. of regression =
14.8
Variables =>
Constant
P
Pc
Y
Coefficients =>
28.84
-2.1235
1.035
3.089
Values =>
240
243
102.4
Q = 87
28.84
-509.64
251.505
316.31
which (by substituting mean values of Pc and Y) can be reduced to the 2-dimensional specification
Qd =
596.66
- 2.1235 P
ASSIGNMENT: Based on your analysis, please assist the company in making a decision about how it might proceed.
Your response should be clearly labelled in four parts as follows.
1) State the assumptions that you are making.
2) Identify whether any of the information given is "irrelevant" to your analysis/decision.
3) Identify at least two approaches to making a decision here.
4) Offer your recommendation to the company's situation.
Period
Q
P
Pc
Y
2011.Q1
64.8
250
250
104
2011.Q2
33.6
265
250
101.5
2011.Q3
37.8
265
240
103
2011.Q4
83.3
240
240
105
2012.Q1
111.7
230
240
100
2012.Q2
137.5
225
260
96.5
2012.Q3
109.5
225
250
93.3
2012.Q4
96.8
220
240
95
2013.Q1
59.5
230
240
97
2013.Q2
83.2
235
250
99
2013.Q3
90.5
245
250
102.5
2013.Q4
105.5
240
240
105
2014.Q1
75.7
250
220
108.5
2014.Q2
91.6
240
230
108.5
2014.Q3
112.7
240
250
108
2014.Q4
102.2
235
240
109
Explanation / Answer
Linear regression analyses are statistical procedures which allow us to move from description to explanation, prediction, and possibly control.Bivariate linear regression analysis is the simplest linear regression procedure.Simple linear regression focuses on explaining/ predicting one of the variables on the basis of information on the other variable.The regression model thus examines changes in one variable as a function of changes or differences in values of the other variable.
The regression model labels variables according to their role:
Dependent Variable (Criterion Variable): The variable whose variation we want to explain or predict. Independent Variable (Predictor Variable): Variable used to predict systematic changes in the dependent/criterion variable.
OLS regression is particularly powerful as it relatively easy to also check the model asumption such as linearity, constant variance and the effect of outliers using simple graphical methods.Below are the assumptions made :
2.The value of F-Statistics is not required here.But since data is computed using SPSS analysis these values are shown.
3..Reports statistic of strength of relationship that are useful for regression analyses with bivariate and multiple predictors. Several correlational indices are presented in the output:
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