Run the diamond regression with all variables simultaneously, then answer the qu

Question

Run the diamond regression with all variables simultaneously, then answer the questions below:

1. Based on the regression results, predict the market value of a diamond with the following characteristics:  

Weight = 1.5 Carats  
Color Grade: E  
Clarity Grade: VS1  
Cut Category: Good  

Submit answer rounded to the nearest dollar without commas or "$".

2. What percentage of the market price behavior do the regression variables appear to explain?

Enter your answer rounded to the nearest whole number without "%". (i.e.: 45.3% is entered as 45)

3. In refining the model with one additional iteration, which regression variable (if any) would be the appropriate choice to remove from the model in an attempt to improve the model?

A. Clarity

B. Cut

C. Carrat

D. Color

E. None of this list (they are all good)

Here is the link to the spreadsheet if needed: https://docs.google.com/spreadsheets/d/1_mXO2S7reRgI261y4raL3icvcQFkPv7QR1LvGYREzKM/edit?usp=sharing

Data from Diamond Buyer's Guide Carat Color Clarity Cut Price $511.00 0.3 VVS1. Very Good 0.3 VS2 Ideal $781.00 0.3 VS2 Ideal $839.00 0.3 VVS1. Ideal $971.00 $1,130.00 0.3 VVS1. Ideal $1,263.00 0.5 SI2 Ideal 0.5 SI1. Ideal $1,604.00 0.5 VS2 Ideal $1,844.00 $2,026.00 0.5 VVS2 Ideal $2,714.00 0.5 VVS2 Ideal VS1. Ideal $5,899.00 $6,445.00 VVS2 Ideal $6,892.00 1.01 VS2 Ideal 1.01 VS1. Ideal $7,308.00 $17,716.00 1.01 Ideal SI2 Very Good $8,620.00 VS2 Very Good $10,264.00 SI1. Premium $11,751.00 S12 Very Good $16,092.00 vsi Very Good $27,080.00 $14,305.00 SI2 Premium SI1. Very Good $17,905.00 3.01 SI1. Very Good $29,396.00 vsz Very Good $42,881.00 $112,079.00 3.01 Good

Explanation / Answer

Solution:

1. The regression equation is Price = 7997.002 + 16186.75Carat - 3827.89Color - 4247.82Clarity + 12135.24Cut

When Carat = 1.5, Color grade, E = 2, Clarity grade, VS1 = 4 and cut category, good = 3, the predicted price would be

Price = 7997.002 + 16186.75 (1.5) - 3827.89 (2) - 4247.82 (4) + 12135.24 (3)

Price = $44,035.81 ~ $44,036

2.

Weight = 1.5 Carats  
Color Grade: E  
Clarity Grade: VS1  
Cut Category: Good

2. Since r-square is 0.8523. 85.23% of the market price behavior do the regression variables appear to explain.

3. Option E is correct.

Since the p-value of all the varables are less than 0.05 significance level, they are significant variables.

SUMMARY OUTPUT Regression Statistics Multiple R 0.923187 R Square 0.852275 Adjusted R Square 0.82273 Standard Error 9708.489 Observations 25 ANOVA df SS MS F Significance F Regression 4 1.09E+10 2.72E+09 28.84662 4.71E-08 Residual 20 1.89E+09 94254749 Total 24 1.28E+10 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 7997.002 8117.446 0.985162 0.336313 -8935.69 24929.7 Carat 16186.75 3122.034 5.184682 4.5E-05 9674.305 22699.2 Color -3827.89 958.8645 -3.9921 0.000717 -5828.04 -1827.73 Clarity -4247.82 1208.817 -3.51403 0.002183 -6769.37 -1726.27 Cut 12135.24 5034.55 2.410393 0.02568 1633.357 22637.13

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