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You will apply the statistical concepts and techniques covered in this week's reading about multiple regression. Specifically, you will look at Step 5 of the
You will apply the statistical concepts and techniques covered in this week's reading about multiple regression. Specifically, you will look at Step 5 of the Python script to answer all questions.
- 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:
- Define the null and alternative hypothesis in mathematical terms and in words.
- Report the level of significance.
- Include the test statistic and the P-value. (Hint: F-Statistic and Prob (F-Statistic) in the output).
- Provide your conclusion and interpretation of the test. Should the null hypothesis be rejected? Why or why not?
- 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.
- 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.
- 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?
- What is the coefficient of determination of your multiple regression model from Module Six? Provide appropriate interpretation of this statistic.
This is my data:
Step1.
Cars data frame (showing only the first five observations)
Unnamed: 0 | mpg | cyl | disp | hp | drat | wt | qsec | vs | am | gear | carb | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
22 | AMC Javelin | 15.2 | 8 | 304.0 | 150 | 3.15 | 3.435 | 17.30 | 0 | 0 | 3 | 2 |
21 | Dodge Challenger | 15.5 | 8 | 318.0 | 150 | 2.76 | 3.520 | 16.87 | 0 | 0 | 3 | 2 |
20 | Toyota Corona | 21.5 | 4 | 120.1 | 97 | 3.70 | 2.465 | 20.01 | 1 | 0 | 3 | 1 |
18 | Honda Civic | 30.4 | 4 | 75.7 | 52 | 4.93 | 1.615 | 18.52 | 1 | 1 | 4 | 2 |
25 | Fiat X1-9 | 27.3 | 4 | 79.0 | 66 | 4.08 | 1.935 | 18.90 | 1 | 1 | 4 | 1 |
Step 2.
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