Use the following data to answer the questions below:

OLS Regression Results ==============================================================================

Dep. Variable: mpg R-squared: 0.840

Model: OLS Adj. R-squared: 0.828

Method: Least Squares F-statistic: 70.64

Date: Mon, 06 Feb 2023 Prob (F-statistic): 1.87e-11

Time: 03:05:42 Log-Likelihood: -69.404

No. Observations: 30 AIC: 144.8

Df Residuals: 27 BIC: 149.0

Df Model: 2

Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975]

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Intercept 37.6181 1.618 23.257 0.000 34.299 40.937

wt -3.8709 0.634 -6.102 0.000 -5.173 -2.569

hp -0.0334 0.009 -3.684 0.001 -0.052 -0.015==============================================================================Omnibus: 4.325 Durbin-Watson: 2.350

Prob(Omnibus): 0.115 Jarque-Bera (JB): 3.132

Skew: 0.782 Prob(JB): 0.209

Kurtosis: 3.246 Cond. No. 588.==============================================================================

mpg= miles per gallon

hp= horsepower of car

wt= weight of car

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. Include the following in your analysis:

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

b. Report the level of significance.

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

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

2) 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,

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