Consumer Reports present weights of a car and total fuel efficiency of automatic transmission new model cars. This data can be used to determine if there is a relationship between the weight of a car and its fuel efficiency. In this case, car weight will be having a varying relationship with fuel efficiency. For instance, the lighter the car, the less fuel it is expected to consume. Therefore, car weight is the explanatory or independent variable, while fuel efficiency is the explained or dependent variable.
These two variables are negatively correlated since an increase in the weight of the car will lead to a decrease in fuel efficiency. Depending on the range of cars used, the relationship can be strong or weak. By squaring the correlation coefficient value, a coefficient of determination (R 2 ) is gotten, which indicates the proportion of the variation in fuel efficiency that can be explained by the weight of the car. The complement of this proportion (1 - R 2 ) is the variation of fuel efficiency that is attributable to chance and other factors other than the car's weight.
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Significance tests help determine if there is a valid correlation at a certain degree of confidence. P values of the coefficient of car weight will act as an indicator as to whether the regression equation is significant. Generally, if the p-value of the coefficient is less than the common alpha (e.g. 0.05 for a 95% confidence interval), the regression model will be significant at that level of confidence (Sullivan, 2019). Otherw ise, the assumption that higher car weights will lead to lower fuel efficiency does not mean that the efficiency values are solely dependent on car weights. Other factors may affect fuel efficiency such as engine capacity, type of fuel used, turbo and supercharging, and several cylinders, among others.
References
Sullivan, L. (2019). Correlation and linear regression. Retrieved from http://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_Correlation-Regression/BS704_Correlation-Regression_print.html
