Introductory econometrics assignment

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. c.

Assume: Null hypothesis: the slope of the relationship of RPRICE2 and log(SAL1) is zero Alternative hypothesis: the slope of the relationship of RPRICE2 and log (SAL1) is not zero By simply looking at the p-value of RPRICE2 is equalled to 0. 0007, which is less than 0. 01 or 1% significant level. Therefore we can reject the Null hypothesis, and conclude that the relationship of RPRICE2 and log (SAL1) is statistically significant or not zero.

This result also indicates that the relationship between RPRICE2 and log (SAL1) is strong, and increase in price of no.1 canned tuna will decrease the unit sales of brand no. 1 canned tuna. The results are consistent with economic theory: increase in price of a particular product will encourage consumer to consume more of its substitute goods and lead to decrease in sale of this particular product. According to the table above, the p-value of RPRICE3 is equalled to 0, which is less than 0. 01 or 1% significant level. Thus we can reject the Null hypothesis, and this indicates that the relationship between RPRICE3 and log (SAL1) is statistically significant or not zero.

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As the result from part (d), there is a negative relationship between RPRICE3 and log (SAL1). This also consistent with the economic theory that increase in price of a particular product will encourage consumers to switch to alternative product and result in decrease in unit sales of this particular product. The results indicate that one unit increase in PR1, PR2 andPR3 together will change SAL1 by between 1. 315% and 13. 712%. 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.

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%.

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