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. 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?
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. 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?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
- 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. - 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?
![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.
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())
Dep. Variable:
Model:
Method:
Date:
Time:
No. Observations:
Df Residuals:
Df Model:
Covariance Type:
Intercept
wt
hp
Omnibus:
Prob (Omnibus):
Skew:
Kurtosis:
coef
Least Squares
Sun, 11 Dec 2022
04:25:46
36.5178
-3.6425
-0.0330
mpg
OLS
std err
nonrobust
1.736
0.686
0.009
30
27
2
R-squared:
Adj. R-squared:
Prob (F-statistic):
F-statistic:
Log-Likelihood:
AIC:
BIC:
t
21.031
-5.312
-3.503
P>|t|
0.000
0.000
0.002
7.195
Durbin-Watson:
0.027 Jarque-Bera (JB):
1.011
Prob(JB):
3.641 Cond. No.
[0.025
32.955
-5.049
-0.052
0.815
0.801
59.52
1.27e-10
-69.947
145.9
150.1
0.975]
40.081
-2.236
-0.014
2.073
5.624
0.0601
624.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc697cfa7-35be-400d-88d6-26bf90a0b862%2Fef5e2d9a-b2a2-42c4-b0d0-4eae823c0804%2Fr24spde_processed.png&w=3840&q=75)
Transcribed Image Text: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.
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())
Dep. Variable:
Model:
Method:
Date:
Time:
No. Observations:
Df Residuals:
Df Model:
Covariance Type:
Intercept
wt
hp
Omnibus:
Prob (Omnibus):
Skew:
Kurtosis:
coef
Least Squares
Sun, 11 Dec 2022
04:25:46
36.5178
-3.6425
-0.0330
mpg
OLS
std err
nonrobust
1.736
0.686
0.009
30
27
2
R-squared:
Adj. R-squared:
Prob (F-statistic):
F-statistic:
Log-Likelihood:
AIC:
BIC:
t
21.031
-5.312
-3.503
P>|t|
0.000
0.000
0.002
7.195
Durbin-Watson:
0.027 Jarque-Bera (JB):
1.011
Prob(JB):
3.641 Cond. No.
[0.025
32.955
-5.049
-0.052
0.815
0.801
59.52
1.27e-10
-69.947
145.9
150.1
0.975]
40.081
-2.236
-0.014
2.073
5.624
0.0601
624.
![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.
# 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)
wt
mpg
hp
mpg 1.000000 -0.855046 -0.788600
wt -0.855046 1.000000 0.670918
hp -0.788600 0.670918 1.000000](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc697cfa7-35be-400d-88d6-26bf90a0b862%2Fef5e2d9a-b2a2-42c4-b0d0-4eae823c0804%2Fs2hbcnr_processed.png&w=3840&q=75)
Transcribed Image Text: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.
# 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)
wt
mpg
hp
mpg 1.000000 -0.855046 -0.788600
wt -0.855046 1.000000 0.670918
hp -0.788600 0.670918 1.000000
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