Answered: Review your peers' calculations and…

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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Your Peer's Data:

In a scatterplot there is a trend that shows the higher the weight of the vehicle the lower the miles per gallon will be. This is what I would expect, as the more weight an engine has to run the more fuel it will use.

The coefficient correlation is -0.866193. the sign is negative reflecting the correlation of weight to miles per gallon. This correlation is not strong, but it does have some correlation. The plot is scattered, and the coefficient is a negative number.

This is how the car companies can use the equations to their advantage. this will show them how the factors correlate with each other and the probabilities and likiehoods of those changes in the variables and what that might do to change the outcomes. This basically includes all of what they need to determine how they can improve their fuel efficiency based on the correlation, using statistical models. The slope coefficient is 0.025 and 0.975 respectively. This is significant as it does cross into the alpha that is 0.05.

My Data:

The x-axis of a scatterplot of the data defines the weight and y-axis of the scatterplot defines the MPG. From my scatterplot, it is clear that as the weight of the car increases the mpg decreases in a moderate linear manner. That is, the graph exhibits a negative linear trend. It is expected that a heavier car needs more fuel to cover a particular distance than a lighter car. That is, as the weight of the car increases the miles per gallon decreases, which is supported by the scatterplot.

Therefore, it is the expected trend.

mpg wt

mpg (Miles per gallon) 1.000000 -0.875315

wt (Weight of the car) -0.875315 1.000000.

The correlation coefficient between the mpg and weight of the car is -0.875315. Since the correlation coefficient lies between -0.7 and 1, it indicates that there is a strong negative relationship between miles per gallon and the weight of the car.

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]

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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

The regression equation by using the output is:

mpg = 37.0899-5.3404*weight

For any value of the weight, fuel efficiency can be predicted. So, car rental companies can use this model to have a better understanding just how fuel efficient each vehicle is. From the regression equation, slope = coefficient of the weight = -5.3404. The null hypothesis for the test is H0: β=0 and the alternative hypothesis is H1: β≠0, where β is the population slope for weight. From the output, the test statistic is -9.579 and the p-value is 0.0. The p-value (0.0) is less than the level of significance (0.05) therefore, the null hypothesis of H0: β=0 must be rejected.

Review your peers' calculations and provide some analysis and interpretation:

1)How do their plots and correlation coefficients compare with yours?

2)Would you recommend this regression model to the car rental company? Why or why not?

Expert Solution