Can You Answer These Questions Please

In your initial post, address the following items:

1. 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. See Step 5 in the Python script. Include the following in your analysis:
2. Define the null and alternative hypothesis in mathematical terms and in words.
3. Report the level of significance.
4. Include the test statistic and the P-value. (Hint: F-Statistic and Prob (F-Statistic) in the output).
5. Provide your conclusion and interpretation of the test. Should the null hypothesis be rejected? Why or why not?
6. What is the slope coefficient for the weight variable? Is this coefficient significant at 5% level of significance (alpha=0.05)? (Hint: Check the P-value,, for weight in Python output. Recall that this is the individual t-test for the beta parameter.) See Step 5 in the Python script.
7. What is the slope coefficient for the horsepower variable? Is this coefficient significant at 5% level of significance (alpha=0.05)? (Hint: Check the P-value,, for horsepower in Python output. Recall that this is the individual t-test for the beta parameter.) See Step 5 in the Python script.
8. What is the purpose of performing individual t-tests after carrying out the overall F-test? What are the differences in the interpretation of the two tests?
9. What is the coefficient of determination of your multiple regression model from Module Six? Provide appropriate interpretation of this statistic.

Results Needed To Answer Questions

Step 5: Multiple regression model to predict miles per gallon using weight and horsepower

This block of code produces a multiple regression model with "miles per gallon" as the response variable, and "weight" and "horsepower" as predictor variables. Theolsmethod in statsmodels.formula.api submodule returns all statistics for this multiple regression model.

Click the block of code below and hit theRunbutton above.

In[5]:

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: 0.822 Model: OLS Adj. R-squared: 0.809 Method: Least Squares F-statistic: 62.23 Date: Thu, 06 Aug 2020 Prob (F-statistic): 7.76e-11 Time: 19:13:24 Log-Likelihood: -69.519 No. Observations: 30 AIC: 145.0 Df Residuals: 27 BIC: 149.2 Df Model: 2 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ Intercept 36.8319 1.734 21.243 0.000 33.274 40.390 wt -3.6736 0.675 -5.441 0.000 -5.059 -2.288 hp -0.0336 0.009 -3.680 0.001 -0.052 -0.015 ============================================================================== Omnibus: 6.279 Durbin-Watson: 1.690 Prob(Omnibus): 0.043 Jarque-Bera (JB): 4.714 Skew: 0.928 Prob(JB): 0.0947 Kurtosis: 3.571 Cond. No. 630. ============================================================================== Warnings: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified.