Editing 2048: Curve-Fitting
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 36: | Line 36: | ||
===Logarithmic=== | ===Logarithmic=== | ||
[[File:Logarithm_plots.png|thumb|200px|Common logarithm functions.]] | [[File:Logarithm_plots.png|thumb|200px|Common logarithm functions.]] | ||
− | <math>f(x) = a\log_b(x)</math> | + | <math>f(x) = a\log_b(x) + c</math> |
A {{w|Logarithm|logarithmic}} curve grows slower on higher values, but still grows without bound to infinity rather than approaching a horizontal {{w|asymptote}}. The small ''b'' in the formula represents the base which is in most cases ''{{w|e (mathematical constant)|e}}'', 10, or 2. If the data presumably does approach a horizontal asymptote then this fit isn't an effective method to explain the nature of the data. | A {{w|Logarithm|logarithmic}} curve grows slower on higher values, but still grows without bound to infinity rather than approaching a horizontal {{w|asymptote}}. The small ''b'' in the formula represents the base which is in most cases ''{{w|e (mathematical constant)|e}}'', 10, or 2. If the data presumably does approach a horizontal asymptote then this fit isn't an effective method to explain the nature of the data. | ||
Line 44: | Line 44: | ||
===Exponential=== | ===Exponential=== | ||
[[File:Exponential.svg|thumb|200px|Exponential growth (green) compared to other functions.]] | [[File:Exponential.svg|thumb|200px|Exponential growth (green) compared to other functions.]] | ||
− | <math>f(x) = a\cdot b^x</math> | + | <math>f(x) = a\cdot b^x + c</math> |
An {{w|Exponential growth|exponential curve}}, on the contrary, is typical of a phenomenon whose growth gets rapidly faster and faster - a common case is a process that generates stuff that contributes to the process itself; think bacteria growth or compound interest. | An {{w|Exponential growth|exponential curve}}, on the contrary, is typical of a phenomenon whose growth gets rapidly faster and faster - a common case is a process that generates stuff that contributes to the process itself; think bacteria growth or compound interest. | ||
Line 59: | Line 59: | ||
===Linear, No Slope=== | ===Linear, No Slope=== | ||
<math>f(x) = c</math> | <math>f(x) = c</math> | ||
− | |||
− | |||
Apparently, the person making this line figured out pretty early on that their data analysis was turning into a scatter plot, and wanted to escape their personal stigma of scatter plots by drawing an obviously false regression line on top of it. Alternatively, they were hoping the data would be flat, and are trying to pretend that there's no real trend to the data by drawing a horizontal trend line. | Apparently, the person making this line figured out pretty early on that their data analysis was turning into a scatter plot, and wanted to escape their personal stigma of scatter plots by drawing an obviously false regression line on top of it. Alternatively, they were hoping the data would be flat, and are trying to pretend that there's no real trend to the data by drawing a horizontal trend line. |