Problem 1: Linear Regression

You are hired by a company Gem Stones co ltd, which is a cubic zirconia manufacturer. You are provided with the dataset containing the prices and other attributes of almost 27,000 cubic zirconia (which is an inexpensive diamond alternative with many of the same qualities as a diamond). The company is earning different profits on different prize slots. You have to help the company in predicting the price for the stone on the bases of the details given in the dataset so it can distinguish between higher profitable stones and lower profitable stones so as to have better profit share. Also, provide them with the best 5 attributes that are most important.

Data Dictionary:

Variable Name	Description
Carat	Carat weight of the cubic zirconia.
Cut	Describe the cut quality of the cubic zirconia. Quality is increasing order Fair, Good, Very Good, Premium, Ideal.
Color	Colour of the cubic zirconia.With D being the best and J the worst.
Clarity	Clarity refers to the absence of the Inclusions and Blemishes. (In order from Best to Worst in terms of avg price) IF, VVS1, VVS2, VS1, VS2, Sl1, Sl2, l1
Depth	The Height of cubic zirconia, measured from the Culet to the table, divided by its average Girdle Diameter.
Table	The Width of the cubic zirconia's Table expressed as a Percentage of its Average Diameter.
Price	the Price of the cubic zirconia.
X	Length of the cubic zirconia in mm.
Y	Width of the cubic zirconia in mm.
Z	Height of the cubic zirconia in mm.

Please explain with python code for the below with detailed explanation so that i can understand practice and do it on my own without any further doubts.

1.1. Read the data and do exploratory data analysis. Describe the data briefly. (Check the null values, Data types, shape, EDA, duplicate values). Perform Univariate and Bivariate Analysis.

1.2 Impute null values if present, also check for the values which are equal to zero. Do they have any meaning or do we need to change them or drop them? Check for the possibility of combining the sub levels of a ordinal variables and take actions accordingly. Explain why you are combining these sub levels with appropriate reasoning.

1.3 Encode the data (having string values) for Modelling. Split the data into train and test (70:30). Apply Linear regression using scikit learn. Perform checks for significant variables using appropriate method from statsmodel. Create multiple models and check the performance of Predictions on Train and Test sets using Rsquare, RMSE & Adj Rsquare. Compare these models and select the best one with appropriate reasoning.

1.4 Inference: Basis on these predictions, what are the business insights and recommendations.

Please explain and summarise the various steps performed in this project. There should be proper business interpretation and actionable insights present.

Dataset for Problem 1: cubic_zirconia.csv

carat	cut	color	clarity	depth	table	x	y	z	price
1	0.3	Ideal	E	SI1	62.1	58	4.27	4.29	2.66	499
2	0.33	Premium	G	IF	60.8	58	4.42	4.46	2.7	984
3	0.9	Very Good	E	VVS2	62.2	60	6.04	6.12	3.78	6289
4	0.42	Ideal	F	VS1	61.6	56	4.82	4.8	2.96	1082
5	0.31	Ideal	F	VVS1	60.4	59	4.35	4.43	2.65	779
6	1.02	Ideal	D	VS2	61.5	56	6.46	6.49	3.99	9502
7	1.01	Good	H	SI1	63.7	60	6.35	6.3	4.03	4836
8	0.5	Premium	E	SI1	61.5	62	5.09	5.06	3.12	1415
9	1.21	Good	H	SI1	63.8	64	6.72	6.63	4.26	5407
10	0.35	Ideal	F	VS2	60.5	57	4.52	4.6	2.76	706
11	0.32	Ideal	E	VS2	61.6	56	4.4	4.43	2.72	637
12	1.1	Premium	D	SI1	60.7	55	6.74	6.71	4.08	6468
13	0.5	Good	E	VS1	61.1	58.2	5.08	5.12	3.11	1932
14	0.71	Ideal	D	SI2	61.6	55	5.74	5.76	3.54	2767
15	1.5	Fair	G	VS2	66.2	53	7.12	7.08	4.7	10644
16	0.31	Ideal	G	VS2	61.6	55	4.37	4.39	2.7	544
17	0.34	Ideal	G	SI1	61.2	57	4.56	4.53	2.78	650
18	1.01	Ideal	D	VS2	59.8	56	6.52	6.49	3.89	7127
19	0.9	Good	D	SI1	61.9	64	6	6.09	3.74	3567
20	0.54	Premium	G	VS2	60	59	5.42	5.22	3.19	1637
21	1.04	Premium	D	VVS2	61.1	60	6.54	6.51	3.99	10984
22	0.4	Ideal	F	VS2	62.9	57	4.72	4.69	2.96	1080
23	1.52	Ideal	D	SI2	62.7	56	7.35	7.28	4.59	8631
24	1.19	Ideal	J	SI2	61.7	56	6.8	6.85	4.21	4508
25	0.66	Ideal	H	SI1	62.4	58	5.53	5.56	3.46	1609
26	1.5	Premium	H	SI2	61.4	62	7.4	7.25	4.49	7187
27	0.34	Ideal	D	SI1		57	4.5	4.44	2.74	803
28	0.52	Ideal	E	VS2	61.5	56	5.18	5.2	3.19	1576
29	0.31	Ideal	H	SI1	61.9	56	4.38	4.35	2.7	595
30	0.71	Good	F	SI2	64	58	5.65	5.59	3.6	1818