import pandas as pdimport statsmodels.formula.api as smimport matplotlib.pyplot as pltX1 = np.random.normal (0, 1, 100)X2 =X1 + 3Y= X1 + X2 + np.random.normal(0, 1, 100)df = pd.DataFrame ({"Y": Y, "X1": X1, "X2": X2})linmodel = sm.ols(formula"YX1 + X2",datadf).fit()linmodel.summary()Output:Intercept-0.0272X11.1074X21.0257Warnings:[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.[2] The smallest eigenvalue is 3.27e-31. This might indicate that there arestrong multicollinearity problems or that the design matrix is singular.Which of the following statements are correct?a) Perfectly correlated regressors X1 and x2 are used.b) Either X1 or X2 should be excluded, as the second regressor does not add any information to the model.6.c) The second warning indicates that the model fit to the data is perfect.

Here Option A will be the right answer Explanation: Generally Multi collinearity problem occurs when…

Perfectly correlated regressors X1 and X2 are used. Either X1 or X2 should be excluded, as the second regressor does not add any The second warning indicates that the model fit to the data is perfect.

Perfectly correlated regressors X1 and X2 are used. Either X1 or X2 should be excluded, as the second regressor does not add any The second warning indicates that the model fit to the data is perfect.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

import pandas as pd
import statsmodels.formula.api as sm
import matplotlib.pyplot as plt
X1 = np.random.normal (0, 1, 100)
X2 =
X1 + 3
Y
= X1 + X2 + np.random.normal(0, 1, 100)
df = pd.DataFrame ({"Y": Y, "X1": X1, "X2": X2})
linmodel = sm.ols(formula
"Y
X1 + X2",
data
df).fit()
linmodel.summary()
Output:
Intercept
-0.0272
X1
1.1074
X2
1.0257
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The smallest eigenvalue is 3.27e-31. This might indicate that there are
strong multicollinearity problems or that the design matrix is singular.
Which of the following statements are correct?
a) Perfectly correlated regressors X1 and x2 are used.
b) Either X1 or X2 should be excluded, as the second regressor does not add any information to the model.
6.
c) The second warning indicates that the model fit to the data is perfect.

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