help with polynomial equations

[lavalounge]

Hello..

I'm way over my head with this one. I havent really used excel to do statistical analysis before. Anyway I did a trendline fit on a dataset and as it turned out, a polynomial equation was the one that had the best fit. When i tried manually plotting the equation, the results were way out of what I would expect. My x would be years 1990 to 2008 and the y would be farm nos.

year farm
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BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" align=right x:num>6059</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; WIDTH: 48pt; HEIGHT: 12.75pt; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" class=xl22 height=17 width=64 align=right x:num>1995</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" align=right x:num>6096</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; WIDTH: 48pt; HEIGHT: 12.75pt; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" class=xl22 height=17 width=64 align=right x:num>1996</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" align=right x:num>5523</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-BOTTOM: #d4d0c8; 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BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" align=right x:num>5971</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; WIDTH: 48pt; HEIGHT: 12.75pt; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" class=xl22 height=17 width=64 align=right x:num>2000</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" align=right x:num>5314</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; WIDTH: 48pt; HEIGHT: 12.75pt; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" class=xl22 height=17 width=64 align=right x:num>2001</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" align=right x:num>4792</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-BOTTOM: #d4d0c8; 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BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" align=right x:num>3451</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; WIDTH: 48pt; HEIGHT: 12.75pt; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" class=xl22 height=17 width=64 align=right x:num>2005</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" align=right x:num>4053</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; WIDTH: 48pt; HEIGHT: 12.75pt; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" class=xl22 height=17 width=64 align=right x:num>2006</TD><TD style="BORDER-BOTTOM: #d4d0c8; BORDER-LEFT: #d4d0c8; BACKGROUND-COLOR: transparent; BORDER-TOP: #d4d0c8; BORDER-RIGHT: #d4d0c8" align=right x:num>3042</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-BOTTOM: #d4d0c8; 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poly y = 4.9148x2 -338.9x + 7947.8​

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R2 = 0.8735​

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Dont know what happened with the equation but the first part should be x to the second power...

newbie here so apologies if i get the terms incorrectly..

hope to hear from you guys... help!!!

cheers,

j

 

[Legacy 14611]

It's not that clear what you expected or just what you want.

However, I charted your data and it looks like a polynomial (of degree >1) doesn't give a better fit than a straight line (i.e. polynomial of degree 1).

Doing the regression fit with farm as dependent and year and year squared as dependent gives the following
farm = 486009 -240.6*year + 4.915 * yearsq
Rsquared = 0.8735

(the intercept here is and should be different from yours coz when squaring years I used deviation from mean, otherwise numerical errors can cause problems).

The so-called "T" or Student/BillGosset ratios, which provide a statistical test whether the values are different from zero are
intercept 10.57 (this not really relevant anyway)
year -10.46
yearsq 1.04

Conclusion, the value for year is significant,that for yearsq is not. (Adding a cubic year likewise turned up no significance for a higher polynomial effect.)

Conclusion: Your farm sales showed a significant linear decline over the years you consider. No adequate evidence of higher polynomial trend.