Question

Click the block of code below and hit the Run button above.

In [6]:

from statsmodels.formula.api import ols

# create the multiple regression model with mpg as the response variable; weight and horsepower as predictor variables.
model = ols('mpg ~ wt+hp', data=cars_df).fit()
print(model.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                    mpg   R-squared:                       0.825
Model:                            OLS   Adj. R-squared:                  0.813
Method:                 Least Squares   F-statistic:                     63.86
Date:                Thu, 13 Feb 2020   Prob (F-statistic):           5.81e-11
Time:                        23:12:29   Log-Likelihood:                -70.042
No. Observations:                  30   AIC:                             146.1
Df Residuals:                      27   BIC:                             150.3
Df Model:                           2                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept     37.1892      1.627     22.862      0.000      33.851      40.527
wt            -3.8068      0.653     -5.831      0.000      -5.146      -2.467
hp            -0.0322      0.010     -3.348      0.002      -0.052      -0.012
==============================================================================
Omnibus:                        4.159   Durbin-Watson:                   2.250
Prob(Omnibus):                  0.125   Jarque-Bera (JB):                3.028
Skew:                           0.772   Prob(JB):                        0.220
Kurtosis:                       3.202   Cond. No.                         563.
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Is at least one of the two variables (weight and horsepower) significant in the model? Run the overall F-test and provide your interpretation at 5% level of significance. Include the following in your analysis:

1. Define the null and alternative hypothesis in mathematical terms and in words.
2. Report the level of significance.
3. Include the test statistic and the P-value. (Hint: F-Statistic and Prob (F-Statistic) in the output).
4. Provide your conclusion and interpretation of the test. Should the null hypothesis be rejected? Why or why not?

Answer 1

From Given output we can

a) Define the null and alternative hypothesis in mathematical terms and in words.

Answer -

H0 : both variables (weight and horsepower) insignificant in the model

Ha :  least one of the two variables (weight and horsepower) significant in the model

b) Report the level of significance

Answer-

level of significance = 5% = 0.05

c) Include the test statistic and the P-value. (Hint: F-Statistic and Prob (F-Statistic) in the output).

Answer -

test statistic = 63.86

P-value = 5.81e-11

d) Provide your conclusion and interpretation of the test. Should the null hypothesis be rejected? Why or why not?

Answer -

Decision Rule : we reject Ho if p-value is less than level of significance.

Conclusion : p -value < 0.05 so we reject H0 hypothesis

Interpretation : There is  least one of the two variables (weight and horsepower) significant in the model

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