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
In this section, you will apply the statistical concepts and techniques covered in this week's reading about
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
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.)
Given that,
Dependent variable (y) = miles per gallon
Independent variable (x) = weight of the car
Level of significance () = 0.05
The correlation and regression output is given.
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