Premium Essay

Diamonds - Should You Buy?

In: Other Topics

Submitted By tony5
Words 595
Pages 3
Data Selection (refer to Excel sheets: Scatter1 and Scatter2)
We used Excel to draw a scatter plot to see the relationship between price and carat. The data presented two different groups of data: 1) Diamonds at low prices with low carat and (2) diamonds at high prices with high carat weight. The data with the diamonds at low prices and low carat is irrelevant so we excluded that portion of the data which had prices under $1000.

Selected data to run the regression
Selected data to run the regression
Cut off point of data at Price = $1000
Cut off point of data at Price = $1000

Variable Grouping and Dummy Variable Assignment The categorical variables: color, clarity, cut, certification, polish, and symmetry were categorized into necessary categories to help simplify the upcoming regression from a very large number of dummy variables.

Then, dummy variables were assigned in accordance to these categories set, per below:

Model

Price= β0 + β1CARAT + β2COLOR_C + β3COLOR_NC+ β4CLARITY_VS + β5CLARITY_SI + β6CUT_I+β7CUT_XV + β8CERT_MR + β9SYM_IXV + β10POLISH_IXV

Model Estimation based on the Professor’s Diamond Engagement Ring:

Linear Model (refer to “Linear” Excel Sheet) β0 + β1CARAT + β2COLOR_C + β3COLOR_NC+ β4CLARITY_VS + β5CLARITY_SI + β6CUT_I+β7CUT_XV + β8CERT_MR + β9SYM_IXV + β10POLISH_IXV= Price

1324.3285+790.5624*0.90+0+0+0+474.6218*1+0+104.3419*1+97.9631*1+0+(35.1454*1)=$2,747.91

Semi-Log Model (refer to “Semi-Log” Excel Sheet)
7.3514+0.3412*0.90+0+0+0+0.1815*1+0+0.0420*1+0.0368*1+0+0.0135*1=7.908
e7.908=$2,718.41

Log-Log Model (refer to “Log-Log” Excel Sheet)
7.6636+0.3300*ln⁡(0.90)+0+0+0+0.1838*1+0+0.0421*1+0.0407*1+0+0.0133*1=7.909
e7.909=$2,721.14

From the linear, semi-log, and log-log models revolving our variables chosen, it is clear to see that the price of the diamond based on the professor’s diamond...

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