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From |
Michael Norman Mitchell <Michael.Norman.Mitchell@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: problem with squared term |

Date |
Sat, 20 Mar 2010 12:06:01 -0700 |

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.

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 ksdtempSource | 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/

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**Follow-Ups**:**Re: st: problem with squared term***From:*Prabhat <prabhat.barnwal@gmail.com>

**References**:**st: problem with squared term***From:*Prabhat <prabhat.barnwal@gmail.com>

**Re: st: problem with squared term***From:*Michael Norman Mitchell <Michael.Norman.Mitchell@gmail.com>

**Re: st: problem with squared term***From:*Prabhat <prabhat.barnwal@gmail.com>

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