Data Analysis and Interpretation

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Data Analysis and Interpretation

   This analysis was done to investigate the relationship between MPG, Cylinders and origin. In this study, I created dummy variables for cylinders and origin. We have five (3, 4, 5, 6, and 8) cylinders classes but class with “4” is used as reference class (i.e. the values in the dummy variables are all zeros for the 4 class cylinder). Also, there are three (AS, EU, and NA) groups of origin but the reference class of origin is “NA”, meaning that the values in the dummy variables are zeros for “NA”. Regression analysis was performed after creating dummy variables for cylinders and origin. In this study, the dependent variable used is “MPG” and the independent variables are “Cylinders” and “Origin”. The data analysis tool in Excel was used to perform the analysis and the result is given below.

Regression analysis table obtained using Data analysis tools in Excel

                                                                          

 

Interpretation

   Regression analysis was performed to examine the relationship between MPG, cylinders and origin. The result in the table above there is a high degree of association between the three variable (Multiple R = 0.8152). Also, the ANOVA table indicates that, overall, the regression model statistically significantly predicts the dependent (MPG) variable (F (8, 391) = 129.152, p < 0.05). This indicates a good fit for the data and regression analysis can be performed.

   Now, looking at the coefficients table, we can see that the two independent (cylinders and origin) are significant because their p-values < 0.05. This implies that the two variables significantly predict MPG. Therefore, the regression model is given as;

MPG = 27.8175 + 10.045(Cylinders_5) + 3.229(Origin_AS)

   This implies that a unit increase in cylinders will increase MPG by 10.045 and a unit increase in origin will increase MPG by 3.229. This is telling us that cylinders have a positive effect on MPG since its coefficient is positive while origin has a positive effect on MPG since its coefficient is positive. Finally, the result indicates that about 66.5% of the total variation in MPG is explained by cylinders and origin because R square value = 0.665.