How to Determine the Equation of a Curved Line of Best Fit?

[F.B]

I really need help. I will try my best to post this chart.

Age/Mass
5/ 24
6 / 25
7 / 27
8 / 28
9 / 31
10 /34
11 /38
12 /41
13 /47
14 /55
The slashes are there to separate the numbers and columns

How would you determine the equation of the line of best fit through these points. Its a curve by the way.

 

[andrevdh]

An exponential fit seems rather close to me. Plot the natural log of the mass versus the age. It more or less conforms to a linear relationship. One would expect that a young boy may sometimes indulges!

 

[quicknote]

I would first plot the data points on a graph and visually inspect if there is a clear trend or pattern. From the given data, it appears that the age is increasing with a corresponding increase in mass, indicating a positive correlation between the two variables.

To determine the equation of the line of best fit, I would use a statistical method called linear regression. This involves finding the line that best represents the relationship between the two variables by minimizing the distance between the line and all the data points.

There are various methods to perform linear regression, such as using a graphing calculator or statistical software. I would input the data points into the chosen method and it would provide me with the equation of the line of best fit.

Since you mentioned that the data points form a curve, I would also consider using polynomial regression, which allows for a curved line of best fit. This method would provide an equation that includes higher-order terms, such as x^2 or x^3, to better fit the curve of the data points.

Overall, determining the equation of the line of best fit through a set of data points involves using statistical methods and considering the type of relationship between the variables, whether it is linear or curved.