The python output below is the result of regressing monthly spot log returns on futures log returns of a stock: OLS Regression Results ============================================================================== Dep. Variable: ret_spot R-squared: 0.989 Model: OLS Adj. R-squared: 0.989 Method: Least Squares F-statistic: 2.147e+04 Date: Thu, 28 May 2020 Prob (F-statistic): 7.54e-240 Time: 23:58:10 Log-Likelihood: -157.16 No. Observations: 246 AIC: 318.3 Df Residuals: 244 BIC: 325.3 Df Model: 1 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ Intercept 0.0131 0.029 0.444 0.658 -0.045 0.071 ret_future 0.9751 0.007 146.543 0.000 0.962 0.988 ============================================================================== Omnibus: 48.818 Durbin-Watson: 2.969 Prob(Omnibus): 0.000 Jarque-Bera (JB): 671.062 Skew: -0.016 Prob(JB): 1.91e-146 Kurtosis: 11.091 Cond. No. 4.45 ============================================================================== Can you claim with 99% confidence that the coefficient for ret_future is not equal to 1? Select one: a. Yes b. No
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We want to test if the coefficient for ret_future is not equal to 1 with 99% confidence. This means we are conducting a two-tailed hypothesis test. Show moreβ¦
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OLS Regression Results Dep. Variable: mpg R-squared: 0.827 Model: OLS Adj. R-squared: 0.814 Method: Least Squares F-statistic: 64.36 Date: Wed, 12 Feb 2020 Prob (F-statistic): 5.33e-11 Time: 16:51:29 Log-Likelihood: -70.390 No. Observations: 30 AIC: 146.8 Df Residuals: 27 BIC: 151.0 Df Model: 2 Covariance Type: nonrobust coef std err t P>|t| [0.025 0.975] Intercept 37.3942 1.661 22.518 0.000 33.987 40.802 wt -3.9512 0.682 -5.796 0.000 -5.350 -2.552 hp -0.0307 0.010 -2.999 0.006 -0.052 -0.010 Omnibus: 4.039 Durbin-Watson: 1.819 Prob(Omnibus): 0.133 Jarque-Bera (JB): 2.994 Skew: 0.771 Prob(JB): 0.224 Kurtosis: 3.140 Cond. No. 565. Warnings: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
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from statsmodels.formula.api import ols # create the simple linear regression model with mpg as the response variable and weight as the predictor variable model = ols('mpg ~ wt', data=cars_df).fit() #print the model summary print(model.summary()) OLS Regression Results ============================================================================== Dep. Variable: mpg R-squared: 0.750 Model: OLS Adj. R-squared: 0.741 Method: Least Squares F-statistic: 84.05 Date: Wed, 05 Feb 2020 Prob (F-statistic): 6.32e-10 Time: 03:12:56 Log-Likelihood: -75.748 No. Observations: 30 AIC: 155.5 Df Residuals: 28 BIC: 158.3 Df Model: 1 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ Intercept 37.2297 1.931 19.282 0.000 33.275 41.185 wt -5.3002 0.578 -9.168 0.000 -6.484 -4.116 ============================================================================== Omnibus: 2.182 Durbin-Watson: 1.825 Prob(Omnibus): 0.336 Jarque-Bera (JB): 1.817 Skew: 0.587 Prob(JB): 0.403 Kurtosis: 2.724 Cond. No. 12.2 ============================================================================== Warnings: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
An economist wishes to study the monthly trend in the Dow Jones Industrial Average (DJIA). Data collected over the past 40 months were used to fit the model E(Yt) = Ξ²0 + Ξ±1t, where y = monthly close of the DJIA and t = month (1, 2, 3, ..., 40). The regression results appear below: Ε· = 88 + 0.25t, RΒ² = 0.37, MSE = 144, F = 4.25, Durbin-Watson d = 0.96 Use the value of the Durbin-Watson test statistic to make a statement about autocorrelation of residuals in the regression model above. There is sufficient evidence (using Ξ± = 0.05) to indicate that positive autocorrelation exists. Approximately 98.5 percent of the residuals lie within two standard deviations of their mean 0. There is insufficient evidence (using Ξ± = 0.05) to indicate that positive autocorrelation exists. Since the value lies in the inconclusive region (using Ξ± = 0.05), we need more information before a definite conclusion can be drawn.
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