3. You have collected data on the prices of diamonds at an online retailer (you

Question

3. You have collected data on the prices of diamonds at an online retailer (you can assume it's a random sample). In particular, you have the price (price) in U.S. dollars and the weight in carats (carats) for 380 diamonds which are of similar clarity and cut (2 measures of diamond quality) The following simple regression was estimated price = 0 + Acarats + u which returned the following estimates (standard errors are in parentheses) price-1679.24 + 5573.34 carats (176.41)(187.14) R2 = 0.647 price= 4036.08

Explanation / Answer

Answers to the question is as follows:

d. Carats.

Since Rsquare for the former equation is higher by a good margin
i.e. .64 vs. .058 we conclude that carats is a stronger determinant.

Please note that Rsquare will give how much of DV variation is explained by IV and hencem
determines how strong determinant is IV.

e.
Lets do this.

>The hypothesis is a 2 sided hypothesis since we want to test if B!=0
If it is statistically significant then it should be b!=0, where b is the coeffficient of
nocolor variable.

>So,

Hypothesis test:
ho: bnocolor=0
ha: bnocolor!=0

> t statistic = (b-0)/SE = (649.95-0)/100.07 =6.5

> Conclusion: Now, a t value of 6.5 is greater than critical value of 1.96. The p-value is 0 which is less than .05, indicating statistically significant variable. Hence, nocolor is statistically significant to determine price

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