A travel agency would like to forecast the number of UK citizen visits abroad so that they can develop a growth plan for their business. The agency’s statistician developed the following model, to be estimated using quarterly data for the past 10 years (40 observations):
where:
•is the number of UK citizen visits abroad during period, measured in millions,
•is an index indicating the period to which the data point corresponds (1, 2, 3, … 40),
•is the Gross Domestic Product (GDP) per capita in the UK for period,
•is a dummy variable equal to one if the observation corresponds to quarter 2 (April-May-June),
•is a dummy variable equal to one if the observation corresponds to quarter 3 (July-August-September), and
•is a dummy variable equal to one if the observation corresponds to quarter 4 (October-November-December).
The results of the model estimation are presented in the following table.
Dependent Variable: VISITS
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Method: Least Squares
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Date: --/--/--Time: --:--
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Sample: 1 40
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Included observations: 40
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Variable
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Coefficient
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Std. Error
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t-Statistic
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Prob.
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C
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95.19166
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45.45449
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2.094219
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0.0438
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TREND
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0.503173
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0.152674
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3.295738
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0.0023
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GDP_PC
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-2.077089
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1.158584
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-1.792783
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0.0819
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Q2
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1.650664
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0.576868
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2.861422
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0.0072
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Q3
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2.674084
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0.578551
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4.622037
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0.0001
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Q4
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0.192040
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0.579254
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0.331531
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0.7423
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R-squared
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0.859137
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Mean dependent var
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19.58068
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Adjusted R-squared
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0.838421
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S.D. dependent var
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3.207040
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S.E. of regression
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1.289129
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Akaike info criterion
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3.483291
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Sum squared resid
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56.50300
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Schwarz criterion
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3.736623
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Log likelihood
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-63.66583
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Hannan-Quinn criter.
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3.574888
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F-statistic
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41.47372
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Durbin-Watson stat
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0.915586
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Prob(F-statistic)
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0.000000
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(a)Report the estimated model in standard form, including standard errors.
(10)
(b)Interpret the estimates of all parameters (including the constant term), paying special attention to the units of measurement of the dependent and independent variables.
(25)
(c)Interpret the number “0.0819” that appears under the “Prob.” column and on the row corresponding to the “GDP_PC” variable on the table above.
(10)
(d)Interpret the F-statistic of the model (clearly state the null and alternative hypotheses and whether you reject the null or not and at what level of significance).
(15)
(e)Interpret the R2of the model.
(10)
(f)Test at the 5% significance level the hypothesis that the parameter associated with the “Q4” variable is greater than 1.0.
(15)
(g)The residuals from the model are plotted against the time index in the figure below. What deviation(s) from the Gauss-Markov assumptions do you identify from this plot? What are the consequences of this deviation for the Ordinary Least Squares estimator, in general?
(15)