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# Problem Description

Your goal is to predict the rate spread of mortgage applications according to the given dataset, which is adapted from the Federal Financial Institutions Examination Council's (FFIEC).

## Target Variable

We're trying to predict the variable rate_spread for each row of the test data set.

1. Train a model using the inputs in train_values.csv and the labels train_labels.csv
2. Predict value for each row in test_values.csv for which you don't know the true value of rate_spread.
3. Output your predictions in a format that matches submission_format.csv exactly.
4. Upload your predictions to this competition in order to get a score.

### Submission Format

The format for the submission file is two columns with row_id and rate_spread. The data type of rate_spread is a float value.

If you predicted 1.0 as the rate spread for each respondent, the .csv file that you submit would look like:

row_id,rate_spread
0,1.0
1,1.0
2,1.0
3,1.0
4,1.0
⁝


### Performance Metric

We're predicting a float value, so this is a regression problem. To measure regression, we'll use a metric known as the "coefficient of determination" or "R squared" (sometimes denoted R2 or r2). R-squared is one metric for evaluating regression models. Informally, r-squared is the proportion of the variance in the dependent variable that is explained by the model. R-squared can be calculated:

$$R^2=1 - \sum_i{(y_i - \hat{y}_i)^2} / \sum_i{(y_i - \bar{y})^2}$$

## Features

There are 21 variables in this dataset. Each row in the dataset represents a HMDA-reported loan application, and the dataset we are working with covers one particular year.

We provide a unique identifier called lender for each individual loan-making institution.

The variables are as follows:

#### Property location

• msa_md (categorical) - A categorical with no ordering indicating Metropolitan Statistical Area/Metropolitan Division where a value of -1 indicates a missing value
• state_code (categorical) - A categorical with no ordering indicating the U.S. state where a value of -1 indicates a missing value
• county_code (categorical) - A categorical with no ordering indicating the county where a value of -1 indicates a missing value

#### Loan information

• lender (categorical) - A categorical with no ordering indicating which of the lenders was the authority in approving or denying this loan

• loan_amount (int) - Size of the requested loan in thousands of dollars

• loan_type (categorical) - Indicates whether the loan granted, applied for, or purchased was conventional, government-guaranteed, or government-insured; available values are:

1 -- Conventional (any loan other than FHA, VA, FSA, or RHS loans)
2 -- FHA-insured (Federal Housing Administration)
4 -- FSA/RHS (Farm Service Agency or Rural Housing Service)

• property_type (categorical) - Indicates whether the loan or application was for a one-to-four-family dwelling (other than manufactured housing), manufactured housing, or multifamily dwelling; available values are:

1 -- One to four-family (other than manufactured housing)
2 -- Manufactured housing
3 -- Multifamily

• loan_purpose (categorical) - Indicates whether the purpose of the loan or application was for home purchase, home improvement, or refinancing; available values are:

1 -- Home purchase
2 -- Home improvement
3 -- Refinancing

• occupancy (categorical) - Indicates whether the property to which the loan application relates will be the owner's principal dwelling; available values are:

1 -- Owner-occupied as a principal dwelling
2 -- Not owner-occupied
3 -- Not applicable

• preapproval (categorical) - Indicate whether the application or loan involved a request for a pre-approval of a home purchase loan; available values are:

1 -- Preapproval was requested
2 -- Preapproval was not requested
3 -- Not applicable


#### Applicant information

• applicant_income (int) - In thousands of dollars

• applicant_ethnicity (categorical) - Ethnicity of the applicant; available values are:

1 -- Hispanic or Latino
2 -- Not Hispanic or Latino
3 -- Information not provided by applicant in mail, Internet, or telephone pplication
4 -- Not applicable
5 -- No co-applicant

• applicant_race (categorical) - Race of the applicant; available values are:

1 -- American Indian or Alaska Native
2 -- Asian
3 -- Black or African American
4 -- Native Hawaiian or Other Pacific Islander
5 -- White
6 -- Information not provided by applicant in mail, Internet, or telephone application
7 -- Not applicable
8 -- No co-applicant

• applicant_sex (categorical) - Sex of the applicant; available values are:

1 -- Male
2 -- Female
3 -- Information not provided by applicant in mail, Internet, or telephone application
4 or 5 -- Not applicable

• co_applicant (bool) - Indicates whether there is a co-applicant (often a spouse) or not

#### Census information

• population - Total population in tract
• minority_population_pct - Percentage of minority population to total population for tract
• ffiecmedian_family_income - FFIEC Median family income in dollars for the MSA/MD in which the tract is located (adjusted annually by FFIEC)
• tract_to_msa_md_income_pct - % of tract median family income compared to MSA/MD median family income
• number_of_owner-occupied_units - Number of dwellings, including individual condominiums, that are lived in by the owner
• number_of_1_to_4_family_units - Dwellings that are built to house fewer than 5 families

#### Index and target variable

• row_id - A unique identifier with no intrinsic meaning, but the IDs in your submission must match the submission format exactly
• rate_spread - Indicates the difference between the offered mortgage rate for the applicant and the standard rate for a comparative mortgage.

### Example Row

Here's an example of one of the rows in the dataset so that you can see the kinds of values you might expect in the dataset. Most are categorical, a few are numerical, and there can be missing values.

row_id 0
loan_type 1
property_type 1
loan_purpose 3
occupancy 1
loan_amount 116
preapproval 3
msa_md 24
state_code 4
county_code 106
applicant_ethnicity 2
applicant_race 3
applicant_sex 2
applicant_income 66
population 3263
minority_population_pct 52.815
ffiecmedian_family_income 71852
tract_to_msa_md_income_pct 81.198
number_of_owner-occupied_units 786
number_of_1_to_4_family_units 1067
lender 494
co_applicant False