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Re: st: problem with squared term
From
Prabhat <[email protected]>
To
[email protected]
Subject
Re: st: problem with squared term
Date
Sun, 21 Mar 2010 04:17:48 +0900
Thanks again Michael !
Given links as well as your web site both seem to be extremely helpful.
Regards,
Prabhat
On Sun, Mar 21, 2010 at 4:06 AM, Michael Norman Mitchell
<[email protected]> wrote:
> Dear Prabhat
>
> These are excellent followup questions...
>
> 1. Why am I not getting this problem with ktotppt and ktotpptsq (here
> totppt is total rainfall)?
>
> I think there are two reasons... 1) that the ktotpptsq effect is much
> smaller (and is not significant), so it means that there is very little
> curvature, and/or 2) possibly because the *zero* value for ktotppt is not as
> far from the mean as it was for temperature.
>
> 2. The coefficient on cw1ksq is significant and positive. So, if I get
> similar result for my variable i.e. kavgtemp, shold I say that it is
> "inverted U" kind of relation (and not linear) ? I mean it is straight
> forward but still would like to confirm if there is some trick.
>
> UCLA ATS has put together a great page on exactly this question. You can
> see it at
>
> http://www.ats.ucla.edu/stat/mult_pkg/faq/general/curves.htm
>
> I hope this helps.
>
> Best regards,
>
> Michael N. Mitchell
> See the Stata tidbit of the week at...
> http://www.MichaelNormanMitchell.com
>
> On 2010-03-20 11.50 AM, Prabhat wrote:
>>
>> Thank you so much Michae!
>> I think your analysis captures it very well.
>>
>> However, I have two new queries-
>> 1. Why am I not getting this problem with ktotppt and ktotpptsq (here
>> totppt is total rainfall)?
>> 2. The coefficient on cw1ksq is significant and positive. So, if I get
>> similar result for my variable i.e. kavgtemp, shold I say that it is
>> "inverted U" kind of relation (and not linear) ? I mean it is straight
>> forward but still would like to confirm if there is some trick.
>>
>> Thanks again!
>>
>> Regards,
>> Prabhat
>>
>>
>> On Sun, Mar 21, 2010 at 3:32 AM, Michael Norman Mitchell
>> <[email protected]> wrote:
>>
>>>
>>> Dear Prabhat
>>>
>>> The coefficient for kavgtemp is the linear effect of average temperature
>>> **when all other variables are held constant at zero**. This influences
>>> the
>>> size of the coefficient when a variable is interacted with (multiplied
>>> by)
>>> other variables. In this case, it is when kavgtemp is multiplied by
>>> itself,
>>> forming the squared term. So, kavgtemp reflects the instantaneous linear
>>> slope when average temperature is equal to 0.
>>>
>>> The because of the squared term, the linear slope will change over the
>>> values of average temp. So, perhaps you might want to see the linear
>>> slope
>>> when the average temp is at the mean. Using the "auto" dataset, here is
>>> an
>>> example showing weight predicting mpg. The first example is like yours,
>>> where the coefficient for weight changes, and the second example uses
>>> centering around the mean.
>>>
>>> . ***
>>> . * Example 1
>>> . clear
>>>
>>> . sysuse auto
>>> (1978 Automobile Data)
>>>
>>> . generate wt1k = weight / 1000
>>>
>>> . generate wt1ksq = wt1k*wt1k
>>>
>>> .
>>> . regress mpg wt1k
>>>
>>> Source | SS df MS Number of obs =
>>> 74
>>> -------------+------------------------------ F( 1, 72) =
>>> 134.62
>>> Model | 1591.99024 1 1591.99024 Prob> F =
>>> 0.0000
>>> Residual | 851.469221 72 11.8259614 R-squared =
>>> 0.6515
>>> -------------+------------------------------ Adj R-squared =
>>> 0.6467
>>> Total | 2443.45946 73 33.4720474 Root MSE =
>>> 3.4389
>>>
>>>
>>> ------------------------------------------------------------------------------
>>> mpg | Coef. Std. Err. t P>|t| [95% Conf.
>>> Interval]
>>>
>>> -------------+----------------------------------------------------------------
>>> wt1k | -6.008687 .5178782 -11.60 0.000 -7.041058
>>> -4.976316
>>> _cons | 39.44028 1.614003 24.44 0.000 36.22283
>>> 42.65774
>>>
>>> ------------------------------------------------------------------------------
>>>
>>> . regress mpg wt1k wt1ksq
>>>
>>> Source | SS df MS Number of obs =
>>> 74
>>> -------------+------------------------------ F( 2, 71) =
>>> 72.80
>>> Model | 1642.522 2 821.261002 Prob> F =
>>> 0.0000
>>> Residual | 800.937455 71 11.2808092 R-squared =
>>> 0.6722
>>> -------------+------------------------------ Adj R-squared =
>>> 0.6630
>>> Total | 2443.45946 73 33.4720474 Root MSE =
>>> 3.3587
>>>
>>>
>>> ------------------------------------------------------------------------------
>>> mpg | Coef. Std. Err. t P>|t| [95% Conf.
>>> Interval]
>>>
>>> -------------+----------------------------------------------------------------
>>> wt1k | -14.15806 3.883535 -3.65 0.001 -21.90161
>>> -6.414512
>>> wt1ksq | 1.324401 .6257594 2.12 0.038 .0766722
>>> 2.57213
>>> _cons | 51.18308 5.767884 8.87 0.000 39.68225
>>> 62.68391
>>>
>>> ------------------------------------------------------------------------------
>>>
>>> . ***
>>> . * Example 2, center wt1k
>>> . summarize wt1k
>>>
>>> Variable | Obs Mean Std. Dev. Min Max
>>> -------------+--------------------------------------------------------
>>> wt1k | 74 3.019459 .7771936 1.76 4.84
>>>
>>> . generate cwt1k = wt1k - r(mean)
>>>
>>> . generate cwt1ksq = cwt1k*cwt1k
>>>
>>> .
>>> . regress mpg cwt1k
>>>
>>> Source | SS df MS Number of obs =
>>> 74
>>> -------------+------------------------------ F( 1, 72) =
>>> 134.62
>>> Model | 1591.99025 1 1591.99025 Prob> F =
>>> 0.0000
>>> Residual | 851.469214 72 11.8259613 R-squared =
>>> 0.6515
>>> -------------+------------------------------ Adj R-squared =
>>> 0.6467
>>> Total | 2443.45946 73 33.4720474 Root MSE =
>>> 3.4389
>>>
>>>
>>> ------------------------------------------------------------------------------
>>> mpg | Coef. Std. Err. t P>|t| [95% Conf.
>>> Interval]
>>>
>>> -------------+----------------------------------------------------------------
>>> cwt1k | -6.008687 .5178782 -11.60 0.000 -7.041058
>>> -4.976316
>>> _cons | 21.2973 .3997628 53.27 0.000 20.50038
>>> 22.09421
>>>
>>> ------------------------------------------------------------------------------
>>>
>>> . regress mpg cwt1k cwt1ksq
>>>
>>> Source | SS df MS Number of obs =
>>> 74
>>> -------------+------------------------------ F( 2, 71) =
>>> 72.80
>>> Model | 1642.52201 2 821.261005 Prob> F =
>>> 0.0000
>>> Residual | 800.93745 71 11.2808092 R-squared =
>>> 0.6722
>>> -------------+------------------------------ Adj R-squared =
>>> 0.6630
>>> Total | 2443.45946 73 33.4720474 Root MSE =
>>> 3.3587
>>>
>>>
>>> ------------------------------------------------------------------------------
>>> mpg | Coef. Std. Err. t P>|t| [95% Conf.
>>> Interval]
>>>
>>> -------------+----------------------------------------------------------------
>>> cwt1k | -6.160112 .5108358 -12.06 0.000 -7.178689
>>> -5.141534
>>> cwt1ksq | 1.324401 .6257594 2.12 0.038 .0766721
>>> 2.57213
>>> _cons | 20.50813 .5398843 37.99 0.000 19.43163
>>> 21.58463
>>>
>>> ------------------------------------------------------------------------------
>>>
>>> Note, now, the coefficient for cwt1k is the linear effect of weight on
>>> mpg
>>> when weight is at the average. If you choose a higher or lower value for
>>> the
>>> centering (say 1sd above the mean, or 1sd below the mean), you will get
>>> different values.
>>>
>>> I hope this helps,
>>>
>>> Michael N. Mitchell
>>> See the Stata tidbit of the week at...
>>> http://www.MichaelNormanMitchell.com
>>>
>>> On 2010-03-20 10.42 AM, Prabhat wrote:
>>>
>>>>
>>>> Dear all,
>>>>
>>>> I have come across a strange problem. I am trying to estimate the
>>>> coefficients for temperature and rainfall using WLS, where my
>>>> dependent variable is rice yield.
>>>> Now, when I am including the square term for the average temperature,
>>>> I am getting a very high and impossible estimate for the temperature
>>>> variable. It should be somewhere between 100-300, but after including
>>>> square term I am getting -3500.
>>>> I have just included OLS results here.
>>>>
>>>> Any comment will be appreciated.
>>>>
>>>>
>>>> Regards,
>>>> Prabhat Barnwal
>>>> International University of Japan
>>>>
>>>>
>>>>
>>>>>
>>>>> . regress kyrice kavgtemp kavgtempsq ktotppt ktotpptsq ksdtemp
>>>>>
>>>>
>>>> Source | SS df MS Number of obs =
>>>> 735
>>>> -------------+------------------------------ F( 5, 729) =
>>>> 13.16
>>>> Model | 21551254.8 5 4310250.95 Prob> F =
>>>> 0.0000
>>>> Residual | 238840813 729 327628.001 R-squared =
>>>> 0.0828
>>>> -------------+------------------------------ Adj R-squared =
>>>> 0.0765
>>>> Total | 260392067 734 354757.585 Root MSE =
>>>> 572.39
>>>>
>>>>
>>>>
>>>> ------------------------------------------------------------------------------
>>>> kyrice | Coef. Std. Err. t P>|t| [95% Conf.
>>>> Interval]
>>>>
>>>>
>>>> -------------+----------------------------------------------------------------
>>>> kavgtemp | -3591.648 855.2294 -4.20 0.000 -5270.655
>>>> -1912.642
>>>> kavgtempsq | 67.01803 15.34115 4.37 0.000 36.89993
>>>> 97.13613
>>>> ktotppt | 1.053627 .5836936 1.81 0.071 -.0922936
>>>> 2.199548
>>>> ktotpptsq | -.0005872 .0003753 -1.56 0.118 -.001324
>>>> .0001496
>>>> ksdtemp | -196.4774 56.57082 -3.47 0.001 -307.5386
>>>> -85.41624
>>>> _cons | 49759.5 11888.92 4.19 0.000 26418.9
>>>> 73100.1
>>>>
>>>>
>>>> ------------------------------------------------------------------------------
>>>> -> . regress kyrice kavgtemp ktotppt ktotpptsq ksdtemp
>>>>
>>>> Source | SS df MS Number of obs =
>>>> 735
>>>> -------------+------------------------------ F( 4, 730) =
>>>> 11.39
>>>> Model | 15298828.3 4 3824707.07 Prob> F =
>>>> 0.0000
>>>> Residual | 245093239 730 335744.163 R-squared =
>>>> 0.0588
>>>> -------------+------------------------------ Adj R-squared =
>>>> 0.0536
>>>> Total | 260392067 734 354757.585 Root MSE =
>>>> 579.43
>>>>
>>>>
>>>>
>>>> ------------------------------------------------------------------------------
>>>> kyrice | Coef. Std. Err. t P>|t| [95% Conf.
>>>> Interval]
>>>>
>>>>
>>>> -------------+----------------------------------------------------------------
>>>> kavgtemp | 143.2145 22.12018 6.47 0.000 99.78776
>>>> 186.6413
>>>> ktotppt | .9560253 .5904461 1.62 0.106 -.2031498
>>>> 2.1152
>>>> ktotpptsq | -.00057 .0003799 -1.50 0.134 -.0013158
>>>> .0001758
>>>> ksdtemp | -213.2879 57.13459 -3.73 0.000 -325.4556
>>>> -101.1202
>>>> _cons | -2107.959 622.1736 -3.39 0.001 -3329.422
>>>> -886.4957
>>>> *
>>>> * For searches and help try:
>>>> * http://www.stata.com/help.cgi?search
>>>> * http://www.stata.com/support/statalist/faq
>>>> * http://www.ats.ucla.edu/stat/stata/
>>>>
>>>
>>> *
>>> * For searches and help try:
>>> * http://www.stata.com/help.cgi?search
>>> * http://www.stata.com/support/statalist/faq
>>> * http://www.ats.ucla.edu/stat/stata/
>>>
>>>
>>
>> *
>> * For searches and help try:
>> * http://www.stata.com/help.cgi?search
>> * http://www.stata.com/support/statalist/faq
>> * http://www.ats.ucla.edu/stat/stata/
>>
>
> *
> * For searches and help try:
> * http://www.stata.com/help.cgi?search
> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
>
*
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