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Introductory econometrics assignment. The reasons for creating these two relative price variables is to demonstrate the impact of relative price changes of no.2 and no.3 canned tuna to the unit sales of brand no.1 canned tuna. As a result of that no.2 an

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Introduction

INTRODUCTORY ECONOMETRICS ASSIGNMENT PART 1 a. By using 'Genr' function from eview, to generate two new relative price variables: RPRICE 2 = APR1/APR2 and RPRICE3 = APR1 / APR3. The reasons for creating these two relative price variables is to demonstrate the impact of relative price changes of no.2 and no.3 canned tuna to the unit sales of brand no.1 canned tuna. As a result of that no.2 and no.3 canned tuna are the substitute goods of no.1 canned tuna. Dependent Variable: LOG(SAL1) Method: Least Squares Date: 10/20/11 Time: 23:05 Sample: 1 52 Included observations: 52 Variable Coefficient Std. Error t-Statistic Prob. C 10.27575 0.518528 19.81716 0.0000 RPRICE2 -1.858067 0.513899 -3.615630 0.0007 R-squared 0.207265 Mean dependent var 8.437187 Adjusted R-squared 0.191410 S.D. dependent var 0.813654 S.E. of regression 0.731651 Akaike info criterion 2.250676 Sum squared resid 26.76564 Schwarz criterion 2.325723 Log likelihood -56.51756 Hannan-Quinn criter. 2.279447 F-statistic 13.07278 Durbin-Watson stat 1.353070 Prob(F-statistic) 0.000696 b. The table above shows the result of estimate function: . is equalled to -1.858067, which means one unit change in RPRICE2 or the relative price change of no.1 and no.2 canned tuna will result in -1.858067 % change in SAL1 or unit sale of no.1 canned tuna. Also, the 95% confidence interval for ?RPRICE2 = [-1.858067 - 1.96*0.513899, -1.858067 + 1.96*0.513899] = [-2.8653,-0.8508]. Thus increase the RPRICE2 by 1 is associated in changing of SAL1 by between -2.8653 and -0.8508 points, with a 95 % confident level. ...read more.

Middle

As increase in price of its substitute goods will encourage consumer to switch their consumption into this particular good. c. For b2, assume H0: =0, H1: <0. With ?=0.05 using the p-value approach. One-side p-value of PR1 = 0.000/2 < 0.05, so reject the null hypothesis. b2 is significantly different away from zero. For b3, assume H0: =0, H1: >0. With ?=0.05 using the p-value approach. One-side p-value of PR2 = 0.1904/2 > 0.05, so fail to reject the null hypothesis. b3 is not significantly different away from zero. For b4, assume H0: =0, H1: >0. With ?=0.05 using the p-value approach. One-side p-value of PR3 = 0.0843/2 < 0.05, so reject the null hypothesis. b4 is significantly different away from zero. d. i. By putting C(2)=300 to do the Wald Test, the probability of t-statistic is equalled to 0.0000. This is less than 0.05 or 5% significant level. There we can reject the null hypothesis, A 1-cent increase in the price of brand one can reduces its sales by 300 cans. ii. By putting C(3)=300 to do the Wald Test, the probability of t-statistic is equalled to 0.0048. This is also less than 0.05 or 5% significant level. We can reject the null hypothesis, A 1-cent increase in the price of brand two increases the sales of brand one by 300 cans. Because the p-value of PR2 is 19% which is not even significant at 10% level, therefore the coefficient of PR2 does not represent the true impact of price change of no.2 canned tuna on unit sales of no.1 canned tuna. ...read more.

Conclusion

This is making more sense while comparing this result with part (a). We can conclude that the increase same amount across the three brands will increase the unit sale of brand by at least 1.314%, compare to part (a) that its results can be positive and negative with a similar range. c. The ln(SAL1) as the dependent variable is a log-linear model, which shows one unit change in PR1, PR2 andPR3 are associated with a percentage change in unit sale of brand one(SAL1 ). This is more preferable in showing the price elasticity of a product and effectively showing the trend of unit sales change. One the other side, the model with SAL1 as the dependent variable is a linear-linear model, which indicates the relationship between one unit changes of PR1, PR2 andPR3 together will result in unit change in SAL1. Summary: According to the results above, we can conclude that there is a positive relationship between the sales on brand no.1 canned tuna and the price of the other two brands canned tuna, also a reverse relationship for the price and unit sales of no.1 canned tuna. If Alpha Supermarket stock all three brands canned tuna with expect sales when no.1 =90, no.2 =75 and no.3= 75, one dollar increase in price for all three brands will be 95% sure that the unit sales for no.1 canned tuna will be increased by 1.3% to 13.7%. ?? ?? ?? ?? ...read more.

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The author has produced excellent regression models and clearly understands what he/she is doing, with good econometric understanding. However, explanations and definitions of variables could make it clearer.

Marked by teacher Nick Simmons 25/03/2012

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