<Student’s name>
<Professor’s name>
In this paper I will check and comment all the steps you did and asked me to review.
- I want you to check my Bangladish excel.xlsx and if I did download it correctly from the website.. The steps are all provided on MBA 5303 Midterm Assignment (1).docx
Well, I went to that site, did everything like was provided in .docx file and downloaded the file named pwt80.xls. As I may see, it is the same, like yours Bangladish excel.xls. So, I think, you downloaded a correct file.
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- Please check my work on excel work.xlsx is it all done in a correct way?? I mean the calculations
Now you take the table given in .doc file adding the income column from the website
But OK, working with this data set. You have created a multiple linear regression, where Qx is a response variable and Px Py Income and Advertising are independent variables.
I did the same, using Excel Tools and obtained the same results.
The regression equation:
QX = 479.7235635 - 1.273897153Px - 0.069742646Py + 0.000212464I + 0.002510614Adv
is correct
(ii) Assume that in 2012 Px, Py, Income, and Advertising are all 10% greater than their 2011 value. Using the estimated equation in the previous part, calculate all the point elasticities of demand (price, income, cross price, and advertising elasticities) in Year 2012. Comment on your results (e.g. is demand for X elastic or inelastic; are X and Y substitutes or complements; is X a normal or an inferior good; is X a luxury or a necessity; is X sensitive to advertising or not).
Now you increase the indicators on 10% (the last row of excel work.xlsx) and using our regression equation you’ve got that
QX = 222.7671765
which is correct value
(iii) Explain how a business may utilize these elasticities to inform its decision-making process
We calculate the price elasticity of Demand using Linear Regression obtained above:
EP=a1*PQ=-1.273897153*233.75222.7671765=-1.33670258
Now estimating the absolute value of EP. As the absolute value of this parameter is higher than 1, this means that the demand is quite elastic, and the amount of demand changes by a larger percentage than the price (it might be goods, which don’t play a significant role for consumer goods, those, which have substitutes). The substitute goods characterized by the fact that the increase in price of one product causes an increase in the consumption of another: reducing the price of one product makes it less desirable to consumers other goods. Examples of such products are: oranges, tangerines, coffee, tea, etc.
Now calculating the Income Elasticity of Demand using the regression equation we have.
EI=a3IQ=0.000212464*272519222.7671765=0.259914758
As we can see, the coefficient of elasticity is between 0 and 1. This good is quite inelastic from the position of the Income Elasticity. This means, that the changes in income shouldn’t significantly change the demand on this good. So, this good might be a necessary good. Since the coefficient in positive, the good is normal and not inferior. According to the definition, “in economics, normal goods are any goods for which demand increases when income increases, and falls when income decreases but price remains constant, i.e. with a positive income elasticity of demand”. According to the definition of inferior good, “an inferior good is a good that decreases in demand when consumer income rises, unlike normal goods, for which the opposite is observed”
The next step is Cross-Price Elasticity of Demand related to the other good (Good Y):
EXY=a2PYQX=-0,0697426463734763*269.5222.7671765=-0.084373485
Important notification. You have written wrong the formula. For this coefficient we have to use ai related to PY. It is a2 in our model. You wrote: Ep = a1*Py/Q which is wrong.
But the calculations are OK.
As EXY<0 we can state, that the goods X and Y are Complements.
Complementary goods (complements) are a few products that complement each other and are consumed at the same time. Examples of such products include: car and gasoline, computer, monitor, keyboard and mouse, pillow and blanket.
Goods are considered complementary, if the value of cross-elasticity is less than zero.
The next step is calculation the Elasticity of Advertisement:
EA=a4AQ=0.002510614*682222.7671765=0.007686225
Please pay attention, there is A, not I.
Since the coefficient of elasticity is between 0 and 1, the demand of the good X is not sensitive to the Advertising. The changes in Advertising will not affect the demand significantly. So, this good might be a necessary good, which doesn’t need to be advertised so much – everybody knows about it.
- (i) Using Excel, transform all variables into natural logarithms (ln). Then use these variables to estimate the demand equation in log-linear form (i.e. ln(Qx) on ln(Px), ln(Py), ln(Income) and ln(Advertising). Write down this estimated equation. (please check my answers)
Now you have calculated the natural logarithms from all values (sheet #2). This is correct.
Sure, the multiple linear regression, according to Excel Tools output is also correct:
LN (QX) = 12.50339114 - 1.678522319 LN (Px) - 0.025620922 LN (Py) + 0.172472876 LN (I) + 0.004578605 LN(Adv)
(ii) Based on the estimated log-linear model, what are the elasticities of demand (price, income, cross price, and advertising elasticities)? Do the conclusions you have reached in Part 1(ii) still hold? Explain your answer
Elasticity |EPx| = 1.678522319
Since the value of the Price Elasticity is higher than 1, it means, that the demand is quite sensitive to the price changes. This might be an evidence of that the good has substitutes or the good is not necessary good.
Elasticity EPy = -0.025620922 Complements
Since the value of Cross-Price Elasticity is lesser than 0, the goods X And Y are complements (as we found out in previous question)
Elasticity of Income = 0.172472876
Since the value of Income Elasticity is positive, the good is normal, not inferior good.
Elasticity of advertising = 0.004578605
Since the Advertising Elasticity is positive and near 0, the conclusions are the same as in previous question – the sensitiveness is very low, the good doesn’t need advertising.
- For each model (linear and log-linear model), investigate which of the explanatory variables are individually statistically significant at the 5% significance level. Explain your answer.
Excel Tools output helps us with the significance. The 95% level of confidence have been already input, and it is much easier to look at p-value of output:
We have to compare which p-values are higher than 0.05. Those variables are insignificant. The variables with p-values <0.05 are significant.
The critical t-value must be calculated for each variable separately. You are testing the significance of each variable, not the whole model significance. But the result is equal to yours:
For log-linear model:
The same result.
- Conduct an F-test (at the 1% significance level) for each model and comment on the results
F test gives us the answer about effectiveness of our whole model, is it significant or not.
And again, Excel Tools have already helped us:
We see here our F-value and significance. As p-value is lower than 0.01, the linear model is significant.
For log-linear model:
The same result, p-value is much lesser than 0.01.
iii) Based on economic theory and the statistical tests you have conducted, which model do you consider preferable (the linear or log-linear model)? Explain fully your answer.
As we can see, the R-square and adjusted R-square of log-linear model is a little better, than in linear. Also the significance of F-test is higher (p-value is lower).
Hence, the log-linear model explains more variability than linear. And so I prefer to use log-linear model.
Well, I wrote this paragraph and only after this I read that you analyzed R-squares too. I think that it is good and our analysis is true.
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