# Linearity in Parameters: Ramsey RESET Test in Python

Last Update: February 21, 2022

Linearity in Parameters: Ramsey RESET Test in Python can be done using `statsmodels` package `linear_reset` function found within `statsmodels.stats.diagnostic` module for evaluating whether linear regression fitted values non-linear combinations explain dependent variable. Main parameters within `linear_reset` function are `res` with original model results, `power` with augmented model added independent variables powers, `test_type` with original model fitted values, independent variables or independent variables first principal component as augmented model added independent variables and `use_f` with logical value on whether an F-test or chi-square test should be done.

As example, we can do Ramsey RESET test on multiple linear regression of house price explained by its lot size and number of bedrooms using data included within `AER` R package `HousePrices` object [1].

First, we import `statmodels` package for data downloading, multiple linear regression fitting and Ramsey RESET test [2].

``````In [1]:
import statsmodels.api as sm
import statsmodels.formula.api as smf
import statsmodels.stats.diagnostic as smd
``````

Second, we create `houseprices` data object using `get_rdataset` function and display first five rows and three columns of data using `print` function and `head` data frame method to view its structure.

``````In [2]:
houseprices = sm.datasets.get_rdataset(dataname="HousePrices", package="AER", cache=True).data
``````
``````Out [2]:
price  lotsize  bedrooms
0  42000.0     5850         3
1  38500.0     4000         2
2  49500.0     3060         3
3  60500.0     6650         3
4  61000.0     6360         2
``````

Third, we fit model with `ols` function using variables within `houseprices` data object and store results within `mlr` object. Within `ols` function, parameter `formula = “price ~ lotsize + bedrooms”` fits model where house price is explained by its lot size and number of bedrooms.

``````In [3]:
mlr = smf.ols(formula="price ~ lotsize + bedrooms", data=houseprices).fit()
``````

Fourth, as example again, we do Ramsey RESET test using `linear_reset` function, store results in `resettest` object and print it. Within `linear_reset` function, parameters `res=mlr` includes original model results, `power=2` adds squared independent variable to augmented model, `test_type="fitted"` adds original model fitted values as augmented model independent variable and `use_f=True` does F-test. Notice that `linear_reset` function parameters `power=2`, `test_type="fitted"` and `use_f=True` were only included as educational examples which can be modified according to your needs.

``````In [4]:
resettest = smd.linear_reset(res=mlr, power=2, test_type="fitted", use_f=True)
print(resettest)
``````
``````Out [4]:
<F test: F=array([[10.63462745]]), p=0.0011796522160904715, df_denom=542, df_num=1>
``````

Courses

My online courses are hosted at Teachable website.

For more details on this concept, you can view my Linear Regression in Python Course.

References

[1] Data Description: Sales prices of houses sold in the city of Windsor, Canada, during July, August and September, 1987.

Original Source: Anglin, P., and Gencay, R. (1996). Semiparametric Estimation of a Hedonic Price Function. Journal of Applied Econometrics, 11, 633–648.

[2] statsmodels Python package: Seabold, Skipper, and Josef Perktold. (2010). “statsmodels: Econometric and statistical modeling with python.” Proceedings of the 9th Python in Science Conference.

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