Answer :
Final answer:
The estimated equation of the line is y = b0 + b1x, with a numeric equation of y = 1.75x. The interpretation of b0 is the y-intercept and the interpretation of b1 is the rate of change between x and y. The R-squared value of 0.73 indicates that 73% of the variation in y can be explained by x. The model's statistical significance depends on the F-test and the coefficients' significance depends on their p-values. Predictive vehicle mileage for specific curb weights can be calculated using the estimated equation. Other independent variables that might explain the dependent variable depend on the specific context.
Explanation:
The estimated equation of the line is written as y = b0 + b1x, where b0 and b1 are the coefficients. The numeric equation for the estimated equation of the line is: y = 1.75x
The interpretation of b0 is that it is the value of y when x is equal to 0. In other words, it represents the y-intercept of the line.
The interpretation of b1 is that it represents the rate of change between the independent variable (x) and the dependent variable (y). In this case, it indicates that for every unit increase in x, y will increase by 1.75.
The numeric value of R-squared is 0.73. Interpreting R-squared means that 73% of the variation in the dependent variable (y) can be explained by the independent variable (x).
To determine if the model is statistically significant, we can use the F-test. Without the specific data and details of the model, it is not possible to provide a definite answer. However, if the p-value associated with the F-test is less than a predetermined level of significance (usually 0.05), we can conclude that the model is statistically significant.
To determine if the coefficients b0 and b1 are statistically significant, we can look at their p-values. If the p-values are less than a predetermined level of significance (usually 0.05), we can conclude that the coefficients are statistically significant. Without the specific data and details of the model, it is not possible to provide a definite answer.
To predict the vehicle mileage (mpg) for a curb weight of 2300lbs. using the regression analysis, we can substitute the value of x into the estimated equation of the line y = b0 + b1x. The predictive vehicle mileage in this case would be 2300 * 1.75 = 4025 miles per gallon.
Similarly, to predict the vehicle mileage (mpg) for a curb weight of 3300lbs., we can substitute the value of x into the estimated equation of the line y = b0 + b1x. The predictive vehicle mileage in this case would be 3300 * 1.75 = 5775 miles per gallon.
In terms of other independent variables that might explain the dependent variable, it would depend on the specific context of the regression analysis and the relationship between the variables being studied. Additional factors such as engine size, aerodynamics, or vehicle type could potentially explain variations in vehicle mileage.
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