Regression Analysis - Run a regression of ‘Average number

Activities

3. Regression analysis.

In this activity, the object is to estimate a demand function. Begin by accessing the data file ‘DataRegression.xlsx’. The data consist of quantity (‘average number of coach seats’) and price (‘average price’). Coach seats refers to the seats on a particular airline.

(a) Run a regression of ‘Average number of coach seats’ on ‘Average Price’. This gives a demand function. Use either the ‘data analysis’ package in Excel or my preference R. Provide the summary statistics. Are the estimated coefficients statistically significant?

 

DataRegression

Year & Quarter  Average number of coach seats                Average Price    Average competitor priceAverage income

Y1, 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

Y2, 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

Y3, 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

Y4, 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

 

(b) Use the demand function to predict the number of seats that would be purchased if the price were to $255 for the four quarters in year 5.

(c) Next regress price on quantity and provide the summary statistics. Are the estimated coefficients statistically significant? Do the estimated coefficients differ once the inverse demand function has been converted back to the normal specification?

(d) Now re-estimate the demand function by including in addition to the ‘average price’, the ‘average competitor price’ and the ‘average income’. Interpret each of the estimated coefficients. Are the estimated coefficients statistically significant? How do the results differ from those in (a)?

(e) Repeat the prediction in (b). Is the prediction the same? If not, why?

(f) Repeat (d) but, instead of quantity Q as the dependent variable, take the natural logarithm of the dependent variable, ln(Q), and make the dependent variable.