mat 243 discussion post based on python script data

Attached is the rubric and the HTML file containing the output data of the python script. This data is needed to answer the below prompts. One to two paragraphs is all that’s needed.

In this discussion, you will apply the statistical concepts and techniques covered in this week’s reading about multiple regression. Last week’s discussion involved a car rental company that wanted to evaluate the premise that heavier cars are less fuel efficient than lighter cars. The company expected fuel efficiency (miles per gallon) and weight of the car (often measured in thousands of pounds) to be correlated. The company also expects cars with higher horsepower to be less fuel efficient than cars with lower horsepower. They would like you to consider this new variable in your analysis.

In this discussion, you will work with a cars data set that includes the three variables used in this discussion:

  • Miles per gallon (coded as mpg in the data set)
  • Weight of the car (coded as wt in the data set)
  • Horsepower (coded as hp in the data set)

The random sample will be drawn from a CSV file. This data will be unique to you, and therefore your answers will be unique as well. Run Step 1 in the Python script to generate your unique sample data.

In your initial post, address the following items:

  1. Check to be sure your scatterplots of miles per gallon against horsepower and weight of the car were included in your attachment. Do the plots show any trend? If yes, is the trend what you expected? Why or why not? See Steps 2 and 3 in the Python script.
  2. What are the coefficients of correlation between miles per gallon and horsepower? Between miles per gallon and the weight of the car? What are the directions and strengths of these coefficients? Do the coefficients of correlation indicate a strong correlation, weak correlation, or no correlation between these variables? See Step 4 in the Python script.
  3. Write the multiple regression equation for miles per gallon as the response variable. Use weight and horsepower as predictor variables. See Step 5 in the Python script. How might the car rental company use this model?
  4. 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:
    1. Define the null and alternative hypothesis in mathematical terms and in words.
    2. Report the level of significance.
    3. Include the test statistic and the P-value. (Hint: F-Statistic and Prob (F-Statistic) in the output).
    4. Provide your conclusion and interpretation of the test. Should the null hypothesis be rejected? Why or why not?