In this section, you will apply the statistical concepts and techniques covered in this week's reading about correlation coefficient and simple linear regression. A car rental company wants to evaluate the premise that heavier cars are less fuel efficient than lighter cars. In other words, the company expects that fuel efficiency (miles per gallon) and weight of the car (often measured in thousands of pounds) are correlated. Performing this analysis will help the company optimize its business model and charge its customers appropriately.

In this discussion, you will work with a cars data set that includes two variables:

Miles per gallon (coded as mpg in the data set)

Weight of the car (coded as wt in the data set)

The random sample was drawn from a CSV file. This data from the Python script is below and will help to answer questions about your unique sample data.

In your post, address the following questions using all the data provided:

Unnamed: 0

mpg

cyl

disp

hp

drat

wt

qsec

vs

am

gear

carb

18

Honda Civic

30.4

4

75.7

52

4.93

1.615

18.52

1

1

4

2

24

Pontiac Firebird

19.2

8

400.0

175

3.08

3.845

17.05

0

0

3

2

5

Valiant

18.1

6

225.0

105

2.76

3.460

20.22

1

0

3

1

6

Duster 360

14.3

8

360.0

245

3.21

3.570

15.84

0

0

3

4

13

Merc 450SLC

15.2

8

275.8

180

3.07

3.780

18.00

0

0

3

3

1) Use the given information below. 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?

mpg wt

mpg 1.000000 -0.875315

wt -0.875315 1.000000

2) Use the info below to 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?

OLS Regression Results: ==============================================================================

Dep. Variable: mpg R-squared: 0.766

Model: OLS Adj. R-squared: 0.758

Method: Least Squares F-statistic: 91.75

Date: Thu, 02 Feb 2023 Prob (F-statistic): 2.47e-10

Time: 23:35:17 Log-Likelihood: -74.862

No. Observations: 30 AIC: 153.7

Df Residuals: 28 BIC: 156.5

Df Model: 1 Covariance Type: nonrobust ==============================================================================

coef std err t P>|t| [0.025 0.975]

------------------------------------------------------------------------------

Intercept 37.0899 1.878 19.750 0.000 33.243 40.937

wt -5.3404 0.558 -9.579 0.000 -6.482 -4.198 ==============================================================================

Omnibus: 4.439 Durbin-Watson: 2.087

Prob(Omnibus): 0.109 Jarque-Bera (JB): 3.332

Skew: 0.812 Prob(JB): 0.189

Kurtosis: 3.175 Cond. No. 12.3 ==============================================================================

3) Using the data provided in question 3, what is the slope coefficient? Is this coefficient significant at a 5% level of significance (alpha=0.05)? (Hint: Check the P-value, P>|t| , for weight in the Python output.)

Question

In this section, you will apply the statistical concepts and techniques covered in this week's reading about correlation coefficient and simple linear regression. A car rental company wants to evaluate the premise that heavier cars are less fuel efficient than lighter cars. In other words, the company expects that fuel efficiency (miles per gallon) and weight of the car (often measured in thousands of pounds) are correlated. Performing this analysis will help the company optimize its business model and charge its customers appropriately.

In this discussion, you will work with a cars data set that includes two variables:

Miles per gallon (coded as mpg in the data set)

Weight of the car (coded as wt in the data set)

The random sample was drawn from a CSV file. This data from the Python script is below and will help to answer questions about your unique sample data.

In your post, address the following questions using all the data provided:

	Unnamed: 0	mpg	cyl	disp	hp	drat	wt	qsec	vs	am	gear	carb
18	Honda Civic	30.4	4	75.7	52	4.93	1.615	18.52	1	1	4	2
24	Pontiac Firebird	19.2	8	400.0	175	3.08	3.845	17.05	0	0	3	2
5	Valiant	18.1	6	225.0	105	2.76	3.460	20.22	1	0	3	1
6	Duster 360	14.3	8	360.0	245	3.21	3.570	15.84	0	0	3	4
13	Merc 450SLC	15.2	8	275.8	180	3.07	3.780	18.00	0	0	3	3

1) Use the given information below. 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?

mpg wt

mpg 1.000000 -0.875315

wt -0.875315 1.000000

2) Use the info below to 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?

OLS Regression Results: ==============================================================================

Dep. Variable: mpg R-squared: 0.766

Model: OLS Adj. R-squared: 0.758

Method: Least Squares F-statistic: 91.75

Date: Thu, 02 Feb 2023 Prob (F-statistic): 2.47e-10

Time: 23:35:17 Log-Likelihood: -74.862

No. Observations: 30 AIC: 153.7

Df Residuals: 28 BIC: 156.5

Df Model: 1 Covariance Type: nonrobust ==============================================================================

coef std err t P>|t| [0.025 0.975]

------------------------------------------------------------------------------

Intercept 37.0899 1.878 19.750 0.000 33.243 40.937

wt -5.3404 0.558 -9.579 0.000 -6.482 -4.198 ==============================================================================

Omnibus: 4.439 Durbin-Watson: 2.087

Prob(Omnibus): 0.109 Jarque-Bera (JB): 3.332

Skew: 0.812 Prob(JB): 0.189

Kurtosis: 3.175 Cond. No. 12.3 ==============================================================================

3) Using the data provided in question 3, what is the slope coefficient? Is this coefficient significant at a 5% level of significance (alpha=0.05)? (Hint: Check the P-value, P>|t| , for weight in the Python output.)

Accepted Answer

Given that,
Dependent variable (y) = miles per gallon
Independent variable (x) = weight of the car…