Question
Can the following questions be addressed? Please: 1.You developed a scatterplot of miles per gallon against weight; check to make sure it was included in
Can the following questions be addressed? Please:
1.You developed a scatterplot of miles per gallon against weight; check to make sure it was included in your attachment. Does the graph show any trend? If yes, is the trend what you expected? Why or why not? See Step 2 in the Python script.
2.What is the coefficient of correlation between miles per gallon and weight? What is the sign of the correlation coefficient? Does the coefficient of correlation indicate a strong correlation, weak correlation, or no correlation between the two variables? How do you know? See Step 3 in the Python script.
3.Write the simple linear regression equation for miles per gallon as the response variable and weight as the predictor variable. How might the car rental company use this model? See Step 4 in the Python script.
4.What is the slope coefficient? Is this coefficient significant at a 5% level of significance (alpha=0.05)? (Hint: Check the P-value,for weight in the Python output.) See Step 4 in the Python script.
Step 1: Generating cars dataset
This block of Python code will generate the sample data for you. You will not be generating the dataset using numpy module this week. Instead, the dataset 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 into a Python dataframe which you will use in later calculations.
Click the block of code below and hit theRunbutton 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 without replacement from mtcars dataset to make the data unique to you.
cars_df = cars_df_orig.sample(n=30, replace=False)
# print only the first five observations in the data set.
print(" Cars data frame (showing only the first five observations)")
display(HTML(cars_df.head().to_html()))
Cars data frame (showing only the first five observations)
Unnamed: 0
mpg
cyl
disp
hp
drat
wt
qsec
vs
am
gear
carb
14
Cadillac Fleetwood
10.4
8
472.0
205
2.93
5.250
17.98
0
0
3
4
13
Merc 450SLC
15.2
8
275.8
180
3.07
3.780
18.00
0
0
3
3
3
Hornet 4 Drive
21.4
6
258.0
110
3.08
3.215
19.44
1
0
3
1
20
Toyota Corona
21.5
4
120.1
97
3.70
2.465
20.01
1
0
3
1
9
Merc 280
19.2
6
167.6
123
3.92
3.440
18.30
1
0
4
4
Step 2: Scatterplot of miles per gallon against weight
The block of code below will develop a scatterplot of 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 theRunbutton above.
NOTE: If the plot is not created, click the code section and hit theRunbutton 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: Correlation coefficient for miles per gallon and weight
Now you will calculate the correlation coefficient between the miles per gallon and weight variables. Thecorrmethod of a dataframe returns the correlation matrix with correlation coefficients between all variables in the dataframe. You will specify to only return the matrix for the variables "miles per gallon" and "weight".
Click the block of code below and hit theRunbutton above.
In[4]:
# create correlation matrix for mpg and wt.
# the correlation coefficient between mpg and wt is contained in the cell for mpg row and wt column (or wt row and mpg column)
mpg_wt_corr = cars_df[['mpg','wt']].corr()
print(mpg_wt_corr)
mpgwt
mpg1.000000 -0.865622
wt-0.8656221.000000
Step 4: Simple linear regression model to predict miles per gallon using weight
The block of code below produces a simple linear regression model using "miles per gallon" as the response variable and "weight" (of the car) as a predictor variable. Theolsmethod in statsmodels.formula.api submodule returns all statistics for this simple linear regression model.
Click the block of code below and hit theRunbutton above.
In[5]:
from statsmodels.formula.api import ols
# create the simple linear regression model with mpg as the response variable and weight as the predictor variable
model = ols('mpg ~ wt', data=cars_df).fit()
#print the model summary
print(model.summary())
OLS Regression Results
==============================================================================
Dep. Variable:mpgR-squared:0.749
Model:OLSAdj. R-squared:0.740
Method:Least SquaresF-statistic:83.69
Date:Wed, 02 Jun 2021Prob (F-statistic):6.62e-10
Time:01:22:43Log-Likelihood:-73.298
No. Observations:30AIC:150.6
Df Residuals:28BIC:153.4
Df Model:1
Covariance Type:nonrobust
==============================================================================
coefstd errtP>|t|[0.0250.975]
------------------------------------------------------------------------------
Intercept35.99981.86019.3510.00032.18939.811
wt-5.01340.548-9.1480.000-6.136-3.891
==============================================================================
Omnibus:2.902Durbin-Watson:2.477
Prob(Omnibus):0.234Jarque-Bera (JB):2.013
Skew:0.633Prob(JB):0.366
Kurtosis:3.095Cond. No.13.0
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
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