**DISCUSSION 1: **

In this discussion you will be interpreting output from your **Python Scripts for the Module Six Discussion.** If you did *not* complete the Module Six discussion, please complete that before working on this assignment.

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Last week’s discussion involved development of a multiple regression model that used miles per gallon as a response variable. Weight and horsepower were predictor variables. You performed an overall F-test to evaluate the significance of your model. This week, you will evaluate the significance of individual predictors. You will use output of Python script from Module Six to perform individual t-tests for each predictor variable. Specifically, you will look at Step 5 of the Python script to answer all questions in the discussion this week.

**In your initial post, address the following items:**

- 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.

Be sure to clearly communicate your ideas using appropriate terminology.

**DISCUSSION 2**

**Use the link in the Jupyter Notebook activity to access your MODULE 8 DISCUSSION Python script**.

In this discussion, you will apply the statistical concepts and techniques covered in this week’s reading about one-way analysis of variance (ANOVA). An investment analyst is evaluating the 10-year mean return on investment for industry-specific exchange-traded funds (ETFs) for three sectors: financial, energy, and technology. The analyst obtains a random sample of 30 ETFs for each sector and calculates the 10-year return of each ETF. The analyst has provided you with this data set. Run Step 1 in the Python script to upload the data file.

Using the sample data, perform one-way analysis of variance (ANOVA). Evaluate whether the average return of *at least one* of the industry-specific ETFs is significantly different. Use a 5% level of significance.

**In your initial post, address the following items:**

- 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. See Step 2 in the Python script.
- Provide your conclusion and interpretation of the test. Should the null hypothesis be rejected? Why or why not?
- Does a side-by-side boxplot of the 10-year returns of ETFs from the three sectors confirm your conclusion of the hypothesis test? Why or why not? See Step 3 in the Python script.

Finally, be sure to review the Discussion Rubric **(ATTACHED)** to understand how you will be graded on this assignment.