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Re: st: problem with squared term


From   Prabhat <prabhat.barnwal@gmail.com>
To   statalist@hsphsun2.harvard.edu
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
<Michael.Norman.Mitchell@gmail.com> 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
>> <Michael.Norman.Mitchell@gmail.com>  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:
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>

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