The demand for roses was estimated using quarterly figures forthe period 1971 (3rd quarter) to 1975 (2nd quarter). Two modelswere estimated and the following results were obtained:
Y = Quantity of roses sold (dozens)
X2 = Average wholesale price of roses ($ perdozen)
X3 = Average wholesale price of carnations ($ perdozen)
X4 = Average weekly family disposable income ($ perweek)
X5 = Time (1971.3 = 1 and 1975.2 = 16)
ln = natural logarithm
The standard errors are given in parentheses.
- lnYt=0.627-1.273 ln X2t + 0.937 lnX3t + 1.713 ln X4t - 0.182
- ln X5t
                                   (0.327)           (0.659)          (1.201)            (0.128)
           R2 =77.8%                             D.W. =1.78                            N = 16
B.       ln YtÙ =10.462 - 1.39 ln X2t
                                     (0.307)
           R2 =59.5%                             D.W. =1.495                          N = 16
Correlation matrix:
| Â Â Â Â Â Â Â Â lnX2 | Â Â Â Â Â Â Â Â lnX3 | Â Â Â Â Â Â Â Â lnX4 | Â Â Â Â Â Â Â Â lnX5 |
ln X2 | Â Â Â Â Â 1.0000 | Â Â Â Â Â Â -.7219 | Â Â Â Â Â Â Â Â Â Â Â .3160 | Â Â Â Â Â Â -.7792 |
ln X3 | Â Â Â Â Â Â -.7219 | Â Â Â Â Â 1.0000 | Â Â Â Â Â Â -.1716 | Â Â Â Â Â Â Â .5521 |
ln X4 | Â Â Â Â Â Â Â .3160 | Â Â Â Â Â Â -.1716 | Â Â Â Â Â 1.0000 | Â Â Â Â Â Â -.6765 |
ln X5 | Â Â Â Â Â Â -.7792 | Â Â Â Â Â Â Â .5521 | Â Â Â Â Â Â -.6765 | Â Â Â Â Â 1.0000 |
a) How would you interpret the coefficients of ln X2,ln X3 and ln X4 in modelA?               Â
What sign would you expect these coefficients to have? Do theresults concur with yourexpectation?                                                                                                                               Â
b) Are these coefficients statisticallysignificant?                                                                  Â
c) Use the results of Model A to test the followinghypotheses:
i) The demand for roses is priceelastic                                                                                 Â
ii) Carnations are substitute goods forroses                                                              Â
iii) Roses are a luxury good (demand increases more thanproportionally as income rises)Â Â
d) Are the results of (b) and (c) in accordance with yourexpectations? If any of the tests are statistically insignificant,give a suggestion as to what may be thereason.                       Â
e) Do you detect the presence of multicollinearity in the data?Explain.                                           Â
f) Do you detect the presence of serial correlation?Explain                                                  Â
g) Do the variables X3, X4 andX5 contribute significantly to the analysis? Test thejoint significance of thesevariables.       Â
h) Starting from model B, assuming that at the time point ofJanuary, 1973, there was a disaster that heavily affected thequantity of roses produced. Suggest a model to check if we have touse two different models for the data before and after thedisaster. (Using dummy variable).
