Module Six Discussion

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Module Six Discussion: Multiple Regression This notebook contains the step-by-step directions for your Module Six discussion. It is very important to run through the steps in order. Some steps depend on the outputs of earlier steps. Once you have completed the steps in this notebook, be sure to answer the questions about this activity in the discussion for this module. Reminder: If you have not already reviewed the discussion prompt, please do so before beginning this activity. That will give you an idea of the questions you will need to answer with the outputs of this script. Initial post (due Thursday) Step 1: Generating cars dataset This block of Python code will generate the sample data for you. You will not be generating the data set using numpy module this week. Instead, the data set will be imported from a CSV file. To make the data unique to you, a random sample of size 30, without replacement, will be drawn from the data in the CSV file. The data set will be saved in a Python dataframe that will be used in later calculations. Click the block of code below and hit the Run button above. In [1]: import pandas as pd from IPython.display import display, HTML # read data from mtcars.csv data set. cars_df_orig = pd.read_csv("https://s3-us-west-2.amazonaws.com/data-analytics.zybooks.com/mtcars.csv") # randomly pick 30 observations from the data set to make the data set unique to you. cars_df = cars_df_orig.sample(n=30, replace= False ) # print only the first five observations in the dataset. print("Cars data frame (showing only the first five observations) \n ") display(HTML(cars_df.head().to_html())) Step 2: Scatterplot of miles per gallon against weight The block of code below will create a scatterplot of the variables "miles per gallon" (coded as mpg in the data set) and "weight" of the car (coded as wt). Click the block of code below and hit the Run button above. NOTE: If the plot is not created, click the code section and hit the Run button again. In [3]: import matplotlib.pyplot as plt # create scatterplot of variables mpg against wt. plt.plot(cars_df["wt"], cars_df["mpg"], 'o', color='red') # set a title for the plot, x-axis, and y-axis. plt.title('MPG against Weight') plt.xlabel('Weight (1000s lbs)') plt.ylabel('MPG') # show the plot. plt.show() Step 3: Scatterplot of miles per gallon against horsepower The block of code below will create a scatterplot of the variables "miles per gallon" (coded as mpg in the data set) and "horsepower" of the car (coded as hp). Click the block of code below and hit the Run button above. NOTE: If the plot is not created, click the code section and hit the Run button again. In [4]: import matplotlib.pyplot as plt # create scatterplot of variables mpg against hp. plt.plot(cars_df["hp"], cars_df["mpg"], 'o', color='blue') # set a title for the plot, x-axis, and y-axis. plt.title('MPG against Horsepower') plt.xlabel('Horsepower') plt.ylabel('MPG') # show the plot. plt.show() Cars data frame (showing only the first five observations) Unnamed: 0 mpg cyl disp hp drat wt qsec vs am gear carb 3 Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1 0 Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4 14 Cadillac Fleetwood 10.4 8 472.0 205 2.93 5.250 17.98 0 0 3 4 16 Chrysler Imperial 14.7 8 440.0 230 3.23 5.345 17.42 0 0 3 4 18 Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2
Step 4: Correlation matrix for miles per gallon, weight and horsepower Now you will calculate the correlation coefficient between the variables "miles per gallon" and "weight". You will also calculate the correlation coefficient between the variables "miles per gallon" and "horsepower". The corr method of a dataframe returns the correlation matrix with the correlation coefficients between all variables in the dataframe. You will specify to only return the matrix for the three variables. Click the block of code below and hit the Run button above. In [5]: # create correlation matrix for mpg, wt, and hp. # The correlation coefficient between mpg and wt is contained in the cell for mpg row and wt column (or wt row and mpg column). # The correlation coefficient between mpg and hp is contained in the cell for mpg row and hp column (or hp row and mpg column). mpg_wt_corr = cars_df[['mpg','wt','hp']].corr() print(mpg_wt_corr) 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. The ols method in statsmodels.formula.api submodule returns all statistics for this multiple regression model. Click the block of code below and hit the Run button above. In [6]: 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()) End of initial post Attach the HTML output to your initial post in the Module Six discussion. The HTML output can be downloaded by clicking File , then Download as , then HTML . Be sure to answer all questions about this activity in the Module Six discussion. Follow-up posts (due Sunday) Return to the Module Six discussion to answer the follow-up questions in your response posts to other students. There are no Python scripts to run for your follow-up posts. mpg wt hp mpg 1.000000 -0.861996 -0.768893 wt -0.861996 1.000000 0.646514 hp -0.768893 0.646514 1.000000 OLS Regression Results ============================================================================== Dep. Variable: mpg R-squared: 0.820 Model: OLS Adj. R-squared: 0.807 Method: Least Squares F-statistic: 61.49 Date: Fri, 04 Aug 2023 Prob (F-statistic): 8.86e-11 Time: 02:10:23 Log-Likelihood: -70.644 No. Observations: 30 AIC: 147.3 Df Residuals: 27 BIC: 151.5 Df Model: 2 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ Intercept 37.2391 1.708 21.799 0.000 33.734 40.744 wt -3.8822 0.663 -5.857 0.000 -5.242 -2.522 hp -0.0318 0.009 -3.397 0.002 -0.051 -0.013 ============================================================================== Omnibus: 4.563 Durbin-Watson: 1.967 Prob(Omnibus): 0.102 Jarque-Bera (JB): 3.511 Skew: 0.835 Prob(JB): 0.173 Kurtosis: 3.132 Cond. No. 590. ============================================================================== Warnings: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
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