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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 03:50:42 +0900

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
>> *
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>
> *
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