Need help with logarithmic trendline

[sgcannon]

I am tracking some events that happen throughout the day. I have modeled the events up to 13:00 with a polynomial trendline. But after 13:00 the frequency of the events taper off until 15:00. So I am trying to track what percentage of the events have happened between the hours of 1300 and 1500 using a logarithmic trendline.

My data points are:


[TABLE="width: 657"]
<tbody>[TR]
[TD="class: xl73, width: 73, align: right"]0.93494[/TD]
[TD="class: xl73, width: 73, align: right"]0.98781[/TD]
[TD="class: xl73, width: 73, align: right"]0.99237[/TD]
[TD="class: xl73, width: 73, align: right"]0.99600[/TD]
[TD="class: xl73, width: 73, align: right"]0.99759[/TD]
[TD="class: xl73, width: 73, align: right"]0.99883[/TD]
[TD="class: xl73, width: 73, align: right"]0.99928[/TD]
[TD="class: xl73, width: 73, align: right"]0.99967[/TD]
[TD="class: xl73, width: 73, align: right"]1.00000[/TD]
[/TR]
[TR]
[TD="class: xl74, align: right"]0.54167[/TD]
[TD="class: xl74, align: right"]0.55208[/TD]
[TD="class: xl74, align: right"]0.56250[/TD]
[TD="class: xl74, align: right"]0.57292[/TD]
[TD="class: xl74, align: right"]0.58333[/TD]
[TD="class: xl74, align: right"]0.59375[/TD]
[TD="class: xl74, align: right"]0.60417[/TD]
[TD="class: xl74, align: right"]0.61458[/TD]
[TD="class: xl74, align: right"]0.62500[/TD]
[/TR]
</tbody>[/TABLE]

The second line are decimal times from 1300 to 1500.

The first line shows what percentage of the events have taken place by the matched time.

So for example, 1500 (.625 in decimal) is the end of the day; therefore, 100% of the events will have taken place by then.

At 1300 (.54167) 93.494% of the events will have taken place.

My problem is that when I select a trendline, the logarithmic version looks just like the linear and is a TERRIBLE fit.

The equation is: y = 0.296ln(x) + 1.1495
and the R^2 is just 0.4813

Admittedly, it's been 30 years since I've done this kind of math but I created a new spreadsheet and filled in numbers that I was sure would make an easy logarithmic trendline.

[TABLE="width: 320"]
<tbody>[TR]
[TD="width: 64, align: right"]9[/TD]
[TD="width: 64, align: right"]9.9[/TD]
[TD="width: 64, align: right"]9.99[/TD]
[TD="width: 64, align: right"]9.999[/TD]
[TD="width: 64, align: right"]9.9999[/TD]
[/TR]
[TR]
[TD="align: right"]10[/TD]
[TD="align: right"]11[/TD]
[TD="align: right"]12[/TD]
[TD="align: right"]13[/TD]
[TD="align: right"]14[/TD]
[/TR]
</tbody>[/TABLE]


But even this one just produces a slightly bent trendline and still has a terrible fit.

What am I doing wrong?

Thanks!

Steve

 

[sgcannon]

Hold on. I'm getting my math confused. the 9, 9.9, 9.99 etc. isn't a logarithmic function is it? That's embarrassing.

And neither are my events/time data points. But it still seems like a logarithmic function would be my best bet to get a decent match. Any mathematicians out there with a little insight?