Need help with determining a math formula

[Todd Burch]

Anyone know how to quickly determine the formula to produce the following values?

This table is a list of acreage sizes and appraised taxable values. As the acreage sizes increase, the $tax/acre decreases. There must be some scaling factor involved.



Acres Taxable Value Tax/Acre
1.536 40,460 26,341
1.582 41,450 26,201
2.037 52,020 25,537
2.623 64,530 24,601
2.529 62,620 24,760
2.592 63,920 24,660
3.73 87,660 23,501
7.17 151,570 21,139
11.423 215,670 18,888
4.277 98,880 23,119
3.251 77,440 23,820
3.133 74,880 23,900
3.41 80,890 23,721
1.781 46,320 26,007
1.617 42,400 26,221
1.602 42,040 26,242

Thanks! Todd

[Jerrimy Snook]

Sorry, I think I got sidetracked... will look at this again...

[Stan Powers]

The math formula is just Taxable Value divided by the Acres. However, the taxable value is based on more than just the acreage, it includes buildings, location, other factors.

Does not appear to be strictly a function of the size of the plot

[Todd Burch]

Hi Stan. Thanks for stepping in.

These values are only property values with no improvements. All are in the same neighborhood. First year to be taxed.

As you can see, the greater the size property, the lower the rate per acre.

Pretend I didn't present the taxable value. That leaves the problem of figuring out a formula for the rate based on the size of property. This is the formula I am trying to determine. The size and rate determine the taxable value - it isn't figured the other way.

[Garrett Ellis]

Are you good with excel? You can plot the data, then have it do a best fit curve. I could do it later... just don't have time at the moment.

[Michael Weber]

Looking at the data I notice that the second item appears to have an incorrect tax per acre value. dividing 41450 by 1.582 does not equal 26257. All the rest work out correctly but I believe that 26257 should be 26201? Something I just noticed putting it into Excel and doing my own division. After that I tried to figure a linear curve fit similar to calculating engineering units from a transducers voltage output (MX+B). That didn't work so looking at sorted values and dividing a tax per acre by the next highest tax per acre value (eliminating the second value) gives a unequal percent increment increase.


1.004567


1.00821


1.018416


1.031371


1.004066


1.002394


1.029338


1.003361


1.004172


1.009364


1.016538


1.093642


1.119656


As the acre size goes up the percent increase may go up or it may go down. So considering that I flunked high school algebra, not really having a clue to whats going on here so I really shouldn't be messing with stuff like this, perhaps some kind of polynomial curve fit might get you close?

[Dale Coons]

Todd,

It's not a linear relationship--so there are probably steps involved, which you won't be able to accurately find from this small data set. It would be best to contact the taxing authority for a tax schedule. As long as you stay in the range of 1.5 to 11.5 acres, you can use a quadratic equation to estimate the tax per acre:

tax= ($61.847 * acres^2) - ($1523.5 * acres) + $28369

A quadratic fit is unreliable outside of the range of data it was fit to as it is a parablola--at some point you will pass the apex and get nonsense values. However, this fit is very, very good for the range of data you provided--it explains about 99 percent of the variation in the values. If I had to guess, there's probably a step right at 7 acres--that is the only value that is not spot on the quadratic regression line.

A linear fit will continue to give a lower tax per acre as the acreage increases, but the fit gets progressively worse at the small and large ends because the relationship isn't linear.

Probably isn't what you're looking for, but might help. if you're trying to figure out what the tax/acre for a certain size property will be.

Dale.

[Todd Burch]

Thanks to all who have responded to this.

I really don't know Excel that well, but I do have it, and I cranked it up and plugged my numbers in and entered a few formulas.

Yes, Michael, you are correct - I had a manual math error. Excel showed it straight away. I edited my post above and gave you credit.

Here's what I have so far, sorted on acres, ascending, echoing y'alls comments and input.

234649

Columns E, F & G are read from the bottom up.

I also entered a formula, illustrating Michael's point about the Tax Rate / Acre percent going up or down (and also a column for the tax rate itself going up or down). The tax rate is supposed to go up the smaller the property one owns. The spreadsheet shows this is not happening for the 2nd entry.

Dale - I'm still absorbing your input. I might have to try my hand at a chart as well.

Thanks all, so far!

Todd

[John Coloccia]

What are you trying to do?

[Todd Burch]

I'm preparing to protest my taxes. My objective is to show unequal and nonuniform taxation. All these properties are in my (new) subdivision, and the assessed values per acre for these properties are DOUBLE surrounding properties. Based on these properties, I'm trying to determine a tax rate schedule and understand the rational used. I think it might be easier to call and just ask.

FWIW, I charted the Tax Rate/Acre % Change. It's all over the board. Excel is kinda cool!

[Matt Meiser]

But wouldn't tax be based on value, not acreage? A 10 acre lot between railroad tracks and the town dump is probably worth less than a 2 on a golf course. And a lot 2x the size of the one next door isn't automatically worth 2x as much.

[Ken Fitzgerald]

Todd,

I think Matt is correct. It's based on "accessed value" for taxes. As Matt indicated the value can vary based on location etc. Keep in mind, however, there is absolutley no connection between tax accessed value and market value. The market value can and often does fluctuate with fluctuations in the local real estate market while the accessed tax value can remain the same.

[Todd Burch]

In Texas, the appraisal district can appraise via different methods. Mass Appraisal is the most common. In our case, someone, (and my district would not disclose who), gave the tax district a list of the sales prices of all the properties sold in my subdivision, so they decided to use Market Value appraisal in our case.

That's why I am pursuing an Equity appeal, not an appeal based on market value. My property is assessed at roughly 164% of equivalent neighboring subdivision properties - and there isn't anywhere near 164% of differences.

I guess that's essentially what I am protesting - the value they are assessing per acre. It's not uniform and equal. In Texas, the law says we can do that.

[Dale Coons]

Todd,

If you want to see why it's not linear, use a 'scatter plot' with no lines, then right click on one of the dots and select 'add trendline', pick polynomial and leave the power set at 2 (higher powers won't help in this case). check the boxes for display equation and show r-squared. You'll see how well it fits.

One other way to look at this which might shed some light on things is to look at the asessed values ordered by time for acreage that are similar in size. If you find that newer assessments (or more recent sales) come in at a lower value (ignoring the possibility of other factors), that would be evidence that you got screwed because no one took (perhaps) falling property values into account and just used the value of the house at the time you bought it or the last assessment.

[Chris Kennedy]

I think I would go with linear for the fit. Unless I have major transcription errors, I get an r-value of 0.997. With a value like that, I would go with a regression fit.

Cheers,

Chris

[Todd Burch]

Here's a scatter plot (dropping the two largest properties, so the data is easier to read.)

234722

I think this scatter plot format will be best for illustrating the disparity of surrounding assessments.

@Chris - I don't understand a word you said! ;)

[Matt Meiser]

Ok, but taxable value is what they determine the value of the propery to be, isn't it? The actual tax isn't in the tens or hundreds of thousands, is it?

[Dale Coons]

Todd,

Add the two points back in, and change the y axis so that it runs from 15K on the bottom instead of 0. (click on the labels to highlight the axis, right click, and somewhere in there is a place you can change the minumum and maximum values for the axis). It will make for a more dramatic visual. Also, if you use the format with no lines (just dots) and add the polynomial trendline, you'll have a smooth curve instead of the jaggies if you care. A straight line regression does happen to have a high r2, but the data isn't linear. It's possibly stepped, but not obviously so. With the two high values added back in, the r2 for a straight line is considerably lower than the quadratic fit, because the data departs from a straight line.

Good luck!
Dale.

[Todd Burch]

Last year my property tax was $528. This year they propose it to be $1320.

[Todd Burch]

I think I've been using the wrong terminology. It's not the tax rate I'm protesting. It's the assessed value of my property.