Can simple volume formulas predict mass of complex diamond shapes?

Can simple volume formulas predict mass of complex diamond shapes?

Author: Tyler Brown

Course Project, UC Irvine, Math 10, W22

Introduction

The project is going to based around the diamonds dataset. We will be looking for a correlation in depth of the diamond and its width (defined by its x-axis times its z-axis) and seeing if we can use that to predict the carat. Since the carat of a diamond is a measure of its weight, we’re essentially looking to see if we can use the dimensions of the diamond to predict the weight of the diamond. Since diamonds are tapered objects and not rectangular prisms, I’m eager to see how the machine does in determining carat.

Beginning of Code

In these following blocks of code, we import all the necessary libraries for this project and the “diamonds” dataset from seaborn.

import numpy as np
import pandas as pd
import seaborn as sns
import altair as alt
#from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import LogisticRegression, LinearRegression
from sklearn.model_selection import train_test_split
#from sklearn.neighbors import KNeighborsClassifier
from sklearn.metrics import log_loss, mean_squared_error
df = sns.load_dataset('diamonds')

Here, we begin to form the dataframe that we will use. We will be making an initial value-chart because we will reuse the initial one for later tests.

valChart = pd.DataFrame([])
valChart["depth"] = df["depth"]
#valChart["table"] = df["table"]
valChart["width"] = df["x"]*df["z"]
valChart["width"] = valChart["width"].map(lambda x: round(x,4))
valChartFirstTest = pd.DataFrame([])
valChartFirstTest = valChart
valChartSecondTest = pd.DataFrame([])
valChartSecondTest = valChart

Here, we are feeding the machine the data it will be predicting with and testing against. We will be predicting data using Linear Regression

X1 = valChartFirstTest[["depth","width"]] 
reg = LinearRegression()
reg.fit(X1, df["carat"])
valChartFirstTest["predicted carat"] = reg.predict(X1)

Now for initializing the training sets, which are randomly chosen rows from our val-chart. The machine learns from the randomly chosen training rows, and tests the machine’s capability for prediction using the remaining rows, the test rows.

X1_train, X1_test, y1_train, y1_test = train_test_split(X1, df["carat"],test_size=0.7)
reg.fit(X1_train, y1_train)
LinearRegression()

These two values here are a mean-squared error, a way of determining the error of predicted numbers compared to the true numbers (lower values means better performance)

mean_squared_error(reg.predict(X1_test),y1_test) 
0.003964498791051252
mean_squared_error(reg.predict(X1_train),y1_train)
0.008806536780164997

As we can see here, the mean squared error is pretty low, however given that the carats are measured to the 100th decimal space, this error is actually mildly high.

To curve this error, I would like to direct your attention to a chart below the following code:

valChartFirstTest["carat"] = df["carat"]
firstChartReduced = pd.DataFrame([])
firstChartReduced = valChartFirstTest
firstChartReduced = firstChartReduced[(df["carat"] < .5) | (df["carat"] >= 1.5) & (df["carat"] <= 2)]
stylingChart = firstChartReduced.style
def highlight_max(s, props=''):
    #print(s.shape)
    if abs(s[0]-s[1])/s[1] > .1:
        return np.where(s > 0, props, '')
    return
stylingChart.apply(highlight_max, props='color:white;background-color:#7300c4', axis=1, subset=["predicted carat", "carat"]);

Narrowing our Data Set

As you’ll see in the chart below here, all lines that are highlighed purple are where the difference between the predicted value and the true value is too high (i.e. when the percent error was above 10%). What you might notice like I did while scrolling through it is that these large errors existed mostly in the lowest values of “carat”, and less in the higher values.

stylingChart
  depth width predicted carat carat
0 61.500000 9.598500 0.150883 0.230000
1 59.800000 8.985900 0.119785 0.210000
2 56.900000 9.355500 0.146736 0.230000
3 62.400000 11.046000 0.230865 0.290000
4 63.300000 11.935000 0.279262 0.310000
5 62.800000 9.771200 0.157938 0.240000
6 62.300000 9.756500 0.158150 0.240000
7 61.900000 10.297100 0.189556 0.260000
8 65.100000 9.636300 0.145512 0.220000
9 59.400000 9.560000 0.153086 0.230000
10 64.000000 11.602500 0.258998 0.300000
11 62.800000 9.667800 0.152090 0.230000
12 60.400000 9.040400 0.121616 0.220000
13 62.200000 11.788500 0.273272 0.310000
14 60.200000 8.603300 0.097314 0.200000
15 60.900000 11.738400 0.273150 0.320000
16 62.000000 11.550800 0.260246 0.300000
17 63.400000 11.421000 0.249986 0.300000
18 63.800000 11.463300 0.251544 0.300000
19 62.700000 11.198600 0.238869 0.300000
20 63.300000 11.544600 0.257184 0.300000
21 63.800000 9.548000 0.143230 0.230000
22 61.000000 9.495400 0.146095 0.230000
23 59.400000 11.501800 0.262899 0.310000
24 58.100000 11.499600 0.265486 0.310000
25 60.400000 9.567700 0.151436 0.230000
26 62.500000 9.805900 0.160526 0.240000
27 62.200000 11.427600 0.252862 0.300000
28 60.500000 9.504000 0.147625 0.230000
29 60.900000 9.583200 0.151269 0.230000
30 60.000000 9.640000 0.156359 0.230000
31 59.800000 9.776800 0.164512 0.230000
32 60.700000 9.607400 0.153055 0.230000
33 59.500000 9.624000 0.156497 0.230000
34 61.900000 9.564800 0.148143 0.230000
35 58.200000 9.622200 0.159107 0.230000
36 64.100000 9.421800 0.135467 0.230000
37 64.000000 11.797500 0.270026 0.310000
38 60.800000 10.407600 0.198099 0.260000
39 61.800000 12.482200 0.313336 0.330000
40 61.200000 12.347500 0.306970 0.330000
41 61.100000 12.392400 0.309718 0.330000
42 65.200000 10.413900 0.189278 0.260000
43 58.400000 10.307400 0.197439 0.260000
44 63.100000 11.935000 0.279679 0.320000
45 62.400000 11.236000 0.241610 0.290000
46 61.800000 11.788500 0.274106 0.320000
47 63.800000 12.164400 0.291192 0.320000
48 63.300000 10.160000 0.178882 0.250000
49 60.700000 11.431200 0.256194 0.290000
50 60.900000 9.849000 0.166301 0.240000
51 61.900000 9.589200 0.149523 0.230000
52 60.900000 12.104000 0.293825 0.320000
53 61.600000 9.471300 0.143481 0.220000
54 59.300000 9.032100 0.123441 0.220000
55 61.000000 11.309000 0.248658 0.300000
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57 62.600000 11.347500 0.247498 0.300000
58 63.000000 11.598800 0.260875 0.300000
59 63.200000 11.475000 0.253457 0.300000
60 60.900000 12.621200 0.323074 0.350000
61 62.600000 11.251800 0.242086 0.300000
62 62.500000 11.540100 0.258598 0.300000
63 62.100000 11.524000 0.258522 0.300000
64 61.500000 14.148800 0.408211 0.420000
65 61.400000 10.810200 0.219616 0.280000
66 62.000000 11.984700 0.284784 0.320000
67 63.300000 11.820900 0.272809 0.310000
68 61.800000 11.658000 0.266726 0.310000
69 60.700000 9.784400 0.163065 0.240000
70 61.500000 9.726500 0.158122 0.240000
71 63.100000 11.583000 0.259773 0.300000
72 62.900000 11.470400 0.253822 0.300000
73 62.500000 11.454300 0.253746 0.300000
74 63.700000 11.641600 0.261835 0.300000
75 59.200000 10.433100 0.202879 0.260000
76 59.900000 10.416500 0.200480 0.260000
77 62.400000 10.444800 0.196866 0.260000
78 62.800000 10.145300 0.179094 0.260000
79 62.600000 10.353000 0.191257 0.260000
80 63.400000 10.200000 0.180936 0.260000
81 62.100000 10.195900 0.183416 0.260000
82 62.900000 10.210800 0.182590 0.260000
83 61.600000 13.345500 0.362575 0.380000
84 57.900000 10.339000 0.200269 0.260000
85 62.300000 9.677500 0.153682 0.240000
86 61.200000 9.784400 0.162022 0.240000
87 60.800000 9.808800 0.164236 0.240000
88 60.700000 10.012200 0.175947 0.240000
89 62.900000 11.875500 0.276732 0.320000
390 62.700000 11.930100 0.280236 0.320000
391 62.800000 12.028600 0.285598 0.320000
392 62.400000 11.886400 0.278391 0.320000
393 61.000000 11.721300 0.271974 0.320000
394 63.100000 12.116400 0.289938 0.320000
395 60.700000 12.069000 0.292263 0.320000
396 60.900000 11.292200 0.247917 0.300000
397 60.100000 11.642400 0.269390 0.300000
398 62.900000 11.470400 0.253822 0.300000
399 63.300000 11.625900 0.261782 0.300000
400 63.800000 11.502000 0.253732 0.300000
401 62.900000 11.400900 0.249892 0.300000
402 63.400000 11.432500 0.250636 0.300000
403 63.900000 12.120800 0.288518 0.320000
404 61.400000 14.307500 0.417395 0.330000
405 61.900000 11.384800 0.251067 0.290000
406 62.400000 11.046000 0.230865 0.290000
407 61.800000 11.577600 0.262179 0.310000
408 61.500000 12.337200 0.305762 0.340000
409 60.400000 12.485000 0.316415 0.340000
410 61.800000 12.454400 0.311764 0.340000
411 62.000000 12.600000 0.319581 0.340000
412 62.300000 11.497200 0.256589 0.300000
413 61.600000 11.246400 0.243866 0.290000
414 60.600000 12.631200 0.324265 0.350000
415 58.400000 14.326000 0.424698 0.430000
416 61.400000 11.799000 0.275534 0.320000
417 61.900000 12.802800 0.331258 0.360000
418 62.000000 11.384800 0.250859 0.300000
419 61.500000 10.306800 0.190939 0.260000
720 62.300000 10.246500 0.185860 0.260000
721 62.100000 10.429500 0.196626 0.260000
722 61.900000 12.933100 0.338627 0.360000
723 57.500000 12.236000 0.308382 0.340000
724 63.300000 12.520800 0.312390 0.340000
725 63.500000 12.565200 0.314484 0.340000
726 63.400000 12.520800 0.312182 0.340000
727 59.600000 12.303400 0.307813 0.340000
728 62.200000 12.471300 0.311885 0.340000
729 64.100000 12.108600 0.287411 0.320000
730 61.600000 11.772000 0.273590 0.310000
731 61.300000 11.684800 0.269284 0.310000
732 62.300000 11.930100 0.281071 0.310000
733 62.000000 11.886400 0.279225 0.310000
734 62.700000 11.777600 0.271612 0.310000
735 62.200000 11.859200 0.277270 0.310000
736 62.200000 11.664000 0.266231 0.310000
737 61.600000 11.701500 0.269603 0.310000
738 61.800000 11.647700 0.266143 0.310000
739 59.400000 12.113600 0.297497 0.330000
740 62.300000 12.182500 0.295345 0.330000
741 62.600000 12.199200 0.295663 0.330000
742 61.900000 12.193000 0.296773 0.330000
743 63.000000 12.287600 0.299828 0.330000
744 62.800000 12.171600 0.293685 0.330000
745 61.500000 12.131200 0.294112 0.330000
746 62.100000 12.210000 0.297317 0.330000
747 63.000000 12.116400 0.290146 0.330000
748 63.600000 12.448300 0.307664 0.330000
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1050 62.900000 12.443400 0.308847 0.330000
1051 61.500000 13.420800 0.367041 0.390000
1052 61.300000 11.995200 0.286838 0.320000
1053 61.200000 10.003500 0.174412 0.250000
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1362 65.600000 34.122000 1.529182 1.500000
1380 60.800000 11.872400 0.280937 0.310000
1381 61.200000 11.667900 0.268537 0.310000
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1384 62.600000 11.777600 0.271821 0.310000
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1386 60.900000 11.667900 0.269163 0.310000
1387 62.400000 9.845600 0.162980 0.240000
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1396 61.800000 9.855300 0.164780 0.240000
1397 61.600000 9.815400 0.162941 0.240000
1398 61.300000 9.840000 0.164957 0.240000
1399 62.300000 12.028600 0.286641 0.320000
1400 61.800000 12.110800 0.292333 0.320000
1401 62.000000 10.206000 0.184195 0.250000
1402 61.500000 10.150000 0.182071 0.250000
1403 61.500000 10.019200 0.174674 0.250000
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1406 61.600000 12.933100 0.339253 0.360000
1407 61.700000 14.071500 0.403423 0.410000
1408 60.200000 11.872400 0.282188 0.320000
1409 61.500000 11.924000 0.282395 0.320000
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1712 63.700000 13.780800 0.382811 0.400000
1713 62.500000 11.750400 0.270491 0.320000
1714 61.400000 11.755300 0.273063 0.320000
1715 59.800000 12.051200 0.293134 0.320000
1716 60.700000 11.792000 0.276598 0.320000
1717 60.200000 11.801400 0.278173 0.320000
1718 63.300000 12.077200 0.287304 0.320000
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1720 61.400000 11.968000 0.285091 0.320000
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2024 57.300000 32.228400 1.439408 1.520000
2025 57.300000 32.228400 1.439408 1.520000
2040 63.200000 12.006000 0.283486 0.320000
2041 61.500000 11.924000 0.282395 0.320000
2042 61.300000 11.951100 0.284344 0.320000
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2048 61.800000 11.913600 0.281181 0.320000
2049 62.400000 11.734300 0.269789 0.320000
2050 63.100000 12.033600 0.285255 0.320000
2051 61.700000 11.913600 0.281389 0.320000
2052 62.000000 11.691000 0.268175 0.320000
2053 62.600000 11.777600 0.271821 0.320000
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2055 62.600000 11.777600 0.271821 0.320000
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2057 62.200000 12.001200 0.285300 0.320000
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2068 61.500000 11.924000 0.282395 0.320000
2069 61.900000 11.815600 0.275430 0.320000
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2388 61.500000 11.924000 0.282395 0.320000
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2397 62.000000 11.886400 0.279225 0.320000
2398 61.300000 10.490200 0.201728 0.260000
2399 61.700000 11.799000 0.274908 0.310000
2411 57.400000 32.432400 1.450736 1.500000
2700 62.200000 11.957400 0.282823 0.310000
2701 62.200000 11.761400 0.271739 0.310000
2702 60.800000 11.694600 0.270882 0.310000
2703 61.100000 11.711600 0.271217 0.310000
2704 62.200000 11.886400 0.278808 0.310000
2705 62.000000 11.718000 0.269702 0.310000
2706 61.300000 11.684800 0.269284 0.310000
2707 62.400000 13.190400 0.352135 0.390000
2708 61.500000 11.203800 0.241666 0.290000
2709 61.600000 12.785500 0.330905 0.350000
2710 61.600000 11.631200 0.265628 0.310000
2711 61.200000 10.265900 0.189252 0.250000
2712 60.900000 11.934000 0.284212 0.320000
2713 61.800000 12.012000 0.286745 0.320000
2714 61.700000 12.138200 0.294091 0.330000
2715 60.600000 12.131200 0.295989 0.330000
2716 61.900000 11.411400 0.252572 0.300000
2717 62.300000 11.470400 0.255074 0.300000
2718 62.500000 11.707200 0.268048 0.320000
2719 63.600000 10.515400 0.198355 0.260000
2720 62.500000 10.378500 0.192908 0.260000
2721 58.900000 10.233600 0.192222 0.260000
2722 60.800000 10.341200 0.194344 0.260000
2723 61.700000 10.322400 0.191404 0.260000
2724 63.300000 10.408500 0.192936 0.260000
2725 61.800000 13.007200 0.343026 0.360000
2726 61.900000 12.628000 0.321373 0.340000
2727 62.600000 12.488000 0.311995 0.340000
2728 61.300000 11.728400 0.271750 0.310000
2729 61.700000 11.842700 0.277380 0.310000
3030 62.200000 11.859200 0.277270 0.310000
3031 61.300000 11.728400 0.271750 0.310000
3032 63.400000 10.434200 0.194180 0.260000
3033 59.800000 10.408200 0.200219 0.260000
3034 64.000000 13.873600 0.387434 0.410000
3035 62.200000 11.664000 0.266231 0.310000
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51986 62.200000 10.170600 0.181776 0.250000
51987 62.200000 10.195900 0.183207 0.250000
51988 61.700000 10.322400 0.191404 0.250000
51989 63.200000 10.029600 0.171717 0.250000
52105 62.100000 15.438000 0.479867 0.470000
52106 62.000000 15.469000 0.481828 0.470000
52290 62.200000 9.910200 0.167050 0.250000
52291 62.100000 10.090200 0.177438 0.250000
52292 62.000000 9.935100 0.168875 0.250000
52293 61.100000 9.954100 0.171827 0.250000
52294 62.800000 10.080000 0.175401 0.250000
52295 64.200000 10.137600 0.175738 0.250000
52296 57.700000 10.025600 0.182963 0.250000
52297 62.600000 9.950000 0.168467 0.250000
52298 59.900000 11.908200 0.284838 0.320000
52299 59.400000 10.094000 0.183285 0.250000
52300 61.200000 11.951100 0.284553 0.320000
52301 61.700000 9.790800 0.161341 0.230000
52302 61.800000 9.613600 0.151111 0.230000
52303 61.400000 9.662400 0.154705 0.230000
52304 61.100000 9.647100 0.154466 0.230000
52305 57.500000 9.984000 0.181027 0.250000
52306 60.800000 11.836000 0.278878 0.320000
52307 58.400000 10.980200 0.235487 0.290000
52308 61.900000 11.815600 0.275430 0.310000
52309 62.300000 11.664000 0.266022 0.310000
52310 58.900000 9.470500 0.149068 0.230000
52311 62.400000 13.392000 0.363535 0.380000
52312 61.400000 11.421500 0.254186 0.300000
52313 60.900000 11.544400 0.262179 0.300000
52314 58.100000 9.652400 0.161023 0.230000
52315 62.200000 11.761400 0.271739 0.320000
52316 63.800000 12.093000 0.287154 0.320000
52317 59.900000 11.854800 0.281819 0.330000
52318 60.900000 11.934000 0.284212 0.330000
52319 62.800000 12.188000 0.294613 0.330000
52377 61.600000 14.847000 0.447487 0.440000
52620 62.900000 12.088800 0.288794 0.320000
52621 63.700000 11.852500 0.273762 0.320000
52622 60.600000 12.086600 0.293467 0.330000
52623 62.500000 11.734300 0.269581 0.310000
52624 60.900000 12.475200 0.314817 0.340000
52625 60.700000 12.230400 0.301391 0.330000
52626 61.100000 12.796000 0.332542 0.360000
52627 63.200000 12.706700 0.323112 0.350000
52628 62.000000 12.510000 0.314491 0.350000
52629 62.100000 12.893600 0.335976 0.370000
52630 60.000000 13.122700 0.353312 0.370000
52631 61.300000 12.049600 0.289915 0.320000
52632 61.600000 12.093900 0.291794 0.330000
52633 61.600000 11.272800 0.245359 0.300000
52634 61.300000 10.624000 0.209294 0.270000
52635 62.200000 9.845600 0.163397 0.240000
52636 62.300000 9.756500 0.158150 0.240000
52637 62.800000 9.835500 0.161574 0.240000
52638 62.000000 9.717000 0.156541 0.240000
52639 60.500000 9.671400 0.157092 0.240000
52640 62.000000 10.707000 0.212528 0.270000
52641 62.900000 9.964700 0.168672 0.240000
52642 60.800000 9.735600 0.160096 0.240000
52643 63.100000 9.760800 0.156724 0.240000
52644 60.300000 9.833200 0.166659 0.240000
52645 60.000000 9.971500 0.175106 0.240000
52646 62.400000 9.820800 0.161577 0.240000
52647 60.900000 9.913800 0.169965 0.240000
52648 61.600000 9.790800 0.161549 0.240000
52649 58.500000 9.615200 0.158085 0.240000
52950 60.600000 9.720000 0.159631 0.240000
52951 62.900000 9.900000 0.165013 0.240000
52952 62.400000 9.771200 0.158772 0.240000
52953 59.200000 9.696000 0.161194 0.240000
52954 59.000000 9.808700 0.167985 0.240000
52955 59.000000 9.720000 0.162969 0.240000
52956 58.700000 9.655600 0.159953 0.240000
52957 61.800000 9.628500 0.151954 0.240000
52958 62.200000 9.935100 0.168458 0.240000
52959 59.700000 9.930800 0.173430 0.240000
52960 63.700000 9.800000 0.157689 0.240000
52961 62.500000 9.860400 0.163608 0.240000
52962 62.700000 9.925000 0.166844 0.240000
52963 60.400000 9.808800 0.165070 0.240000
52964 60.000000 9.971500 0.175106 0.240000
52965 60.700000 9.671400 0.156674 0.240000
52966 61.100000 9.954100 0.171827 0.240000
52967 62.600000 9.707100 0.154730 0.240000
52968 61.800000 9.805900 0.161986 0.240000
52969 61.600000 9.960000 0.171118 0.240000
52970 62.200000 13.847400 0.389706 0.400000
52971 61.100000 13.224000 0.356746 0.370000
52972 62.100000 13.156000 0.350815 0.370000
52973 60.900000 13.102900 0.350315 0.370000
52974 61.500000 12.757400 0.329525 0.350000
52975 58.300000 9.840000 0.171215 0.240000
52976 63.000000 11.363200 0.247551 0.300000
52977 61.800000 12.802800 0.331467 0.350000
52978 59.700000 11.284000 0.249956 0.300000
52979 61.000000 11.309000 0.248658 0.300000
53280 63.100000 11.598800 0.260666 0.300000
53281 62.200000 11.305000 0.245929 0.300000
53282 62.600000 11.320800 0.245988 0.300000
53283 62.000000 11.289000 0.245441 0.300000
53284 62.400000 11.209500 0.240111 0.300000
53285 62.600000 11.347500 0.247498 0.300000
53286 62.500000 11.374200 0.249216 0.300000
53287 62.100000 11.593900 0.262475 0.300000
53288 61.000000 11.352000 0.251090 0.300000
53289 63.700000 12.857600 0.330603 0.350000
53290 62.300000 11.470400 0.255074 0.300000
53291 63.300000 11.641600 0.262670 0.300000
53292 61.900000 11.550800 0.260455 0.300000
53293 63.300000 11.309600 0.243894 0.300000
53294 60.500000 11.318400 0.250233 0.300000
53295 61.400000 11.368500 0.251189 0.300000
53296 63.800000 11.463300 0.251544 0.300000
53297 61.700000 11.507700 0.258435 0.300000
53298 61.200000 11.187400 0.241364 0.300000
53299 61.400000 11.491200 0.258127 0.300000
53300 62.800000 11.363200 0.247969 0.300000
53301 61.300000 11.421500 0.254394 0.300000
53302 62.200000 11.497200 0.256798 0.300000
53303 61.600000 11.368500 0.250771 0.300000
53304 62.500000 11.443600 0.253141 0.300000
53305 62.300000 11.427600 0.252653 0.300000
53306 63.400000 11.544600 0.256976 0.300000
53307 62.300000 11.140800 0.236434 0.300000
53308 62.700000 11.251800 0.241877 0.300000
53309 62.500000 11.278400 0.243799 0.300000
53456 60.600000 15.697200 0.497654 0.480000
53610 61.600000 12.757400 0.329316 0.350000
53611 59.600000 12.521800 0.320164 0.350000
53612 62.200000 11.427600 0.252862 0.300000
53613 62.200000 11.236000 0.242027 0.300000
53614 62.200000 11.427600 0.252862 0.300000
53615 62.400000 11.567000 0.260328 0.300000
53616 62.100000 11.262500 0.243734 0.300000
53617 61.000000 11.144700 0.239367 0.300000
53618 61.900000 11.384800 0.251067 0.300000
53619 61.100000 11.448000 0.256310 0.300000
53620 63.200000 11.405600 0.249532 0.300000
53621 61.100000 12.565600 0.319513 0.350000
53622 63.800000 11.657100 0.262503 0.300000
53623 62.200000 11.427600 0.252862 0.300000
53624 62.000000 11.524000 0.258731 0.300000
53625 63.100000 11.529000 0.256719 0.300000
53626 60.700000 12.548100 0.319357 0.350000
53627 61.300000 11.203800 0.242083 0.300000
53628 61.700000 11.342000 0.249064 0.300000
53629 61.800000 12.555000 0.317453 0.350000
53630 60.600000 11.223000 0.244629 0.300000
53631 61.000000 11.501000 0.259516 0.300000
53632 61.100000 11.378400 0.252374 0.300000
53633 61.900000 11.577600 0.261971 0.300000
53634 61.600000 11.438000 0.254702 0.300000
53635 62.100000 11.524000 0.258522 0.300000
53636 61.600000 11.342000 0.249273 0.300000
53637 62.500000 11.374200 0.249216 0.300000
53638 61.000000 11.282700 0.247171 0.300000
53639 61.000000 11.571000 0.263475 0.300000

Due to this, I decided to do some tests where I narrowed down the values of our training set to carat values between .75 and 2 in the following code.

valChartSecondTest = valChartSecondTest[(df["carat"] >= .75) & (df["carat"] <= 2)]
y2 = df["carat"][(df["carat"] >= .75) & (df["carat"] <= 2)]
y2 = y2[valChartSecondTest["width"] != 0]
valChartSecondTest = valChartSecondTest[valChartSecondTest["width"] != 0]

Again, we will train the machine and test.

X2 = valChartSecondTest[["depth","width"]]
reg = LinearRegression()
reg.fit(X2, y2)
valChartSecondTest["predicted carat"] = reg.predict(X2)
X2_train, X2_test, y2_train, y2_test = train_test_split(X2, y2,test_size=0.7)
reg.fit(X2_train, y2_train)
LinearRegression()
mean_squared_error(reg.predict(X2_test),y2_test)
0.0011296180202952503
mean_squared_error(reg.predict(X2_train),y2_train)
0.0007062673697986459

As you can see, the error is now a fraction of what it was in the previous test after we narrowed down the sample size. I believe this is due to the dimensions of the diamond relating to the volume differently as size increases. So narrowing down the volume would be more beneficial

Below I’m going to remove the data’s outliers (that seem to appear due to human errors while inputing data) and graph our predicted carats vs our true carats.

valChartSecondTest = valChartSecondTest[valChartSecondTest["width"].between(valChartSecondTest["width"].quantile(.15), valChartSecondTest["width"].quantile(.85))]
valChartSecondTest = valChartSecondTest[valChartSecondTest["carat"].between(valChartSecondTest["carat"].quantile(.05), valChartSecondTest["carat"].quantile(.95))]
alt.data_transformers.disable_max_rows()
alt.Chart(valChartSecondTest).mark_bar().encode(
    x="width",
    y="depth",
    color = "predicted carat"

).properties(
    title=f"Second Test Predicted Carat with {valChart.size} Bars",
    #width=alt.Step(100)
    width=1200,
    height = 1000
    
)
alt.Chart(valChartSecondTest).mark_bar().encode(
    x="width",
    y="depth",
    color = "carat"

).properties(
    title=f"Second Test True Carat with {valChart.size} Bars",
    width=1200,
    height = 1000
    
)

As you can see from these graphs, the Predicted Carat graph shows a similar gradient to that of the True Carats, which indicates we were successful in showing the machine a corrolation between weight and carats.

Also, the width was probably the more important factor when predicting carat, as I can’t see as much change in color (which relates to carat) as I do for width. Due to this, I looked at the co-efficients the regression curve took:

reg.coef_
array([-0.00176098,  0.06315282])

As you can see, the first coefficient (relating to depth) was about 100 times smaller than that relating to the second coefficient (width), so width played a much bigger part in determining weight of a diamond.

Summary

We showed that we can somewhat reliably determine the weight of a diamond given its dimensions by visualizing our performance through graphs and the mean-squared-error test. We noticed that we can get an even better estimate of the weights when we narrow down the tests to closer to the median of true carats. Naturally, volume of the diamond would relate to its weight, however since the diamond isn’t a perfect rectangular prism, the weight won’t perfectly relate to the weight, but it’s good we could make close estimates.

References

The dataset is from seaborn

Most of the code is from the course

Code relating to the variable “stylingChart” was sourced from Pandas documentation on Styles and Apply: https://pandas.pydata.org/docs/reference/api/pandas.Series.apply.html#pandas.Series.apply

https://pandas.pydata.org/pandas-docs/stable/user_guide/style.html#Table-Styles

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