Hello,
I'm currently writing a bachelor' thesis on determinant of demand for higher education. I have several independent variables, including ln expenditure per capita and ln expenditure per capita^2 to show diminishing marginal utility of educational expenditure. I have estimated the turning point of ln expenditure per capita^2 with: exp(-coefficient of the linear term/(2*coefficient of the squared term) and the result is =EXP(4.215897/(2*0.1161465)) = 76.213.474. This value does not lie within the range of data because the maximum value of expenditure per capita is 4.245.910.
Is it okay to have turning point that does not lie within the range of data? Or is it another way to estimate the turning point? And how to make a graph from quadratic function?
I would really appreciate any insight into my problem.
logit pt lncost lnopt_cost lnexpend_cap lnexpend_cap2 i.educhead i.socact i.lcc i.gender
Iteration 0: log likelihood = -7098.044
Iteration 1: log likelihood = -6208.2584
Iteration 2: log likelihood = -6166.0261
Iteration 3: log likelihood = -6165.5927
Iteration 4: log likelihood = -6165.5926
Logistic regression Number of obs = 12984
LR chi2(9) = 1864.90
Prob > chi2 = 0.0000
Log likelihood = -6165.5926 Pseudo R2 = 0.1314
pt Coef. Std. Err. z P>z [95% Conf. Interval]
lncost -.5694564 .0905392 -6.29 0.000 -.74691 -.3920029
lnopt_cost -.4964979 .0484262 -10.25 0.000 -.5914115 -.4015843
lnexpend_cap 4.215897 1.344818 3.13 0.002 1.580103 6.851692
lnexpend_cap2 -.1161465 .049625 -2.34 0.019 -.2134097 -.0188834
educhead
PT 1.674627 .080819 20.72 0.000 1.516224 1.833029
socact
Mengikuti Salah Satu K.. -.0138342 .0621084 -0.22 0.824 -.1355645 .1078962
Mengikuti Kedua Kegiat.. .10826 .057488 1.88 0.060 -.0044143 .2209343
lcc
Perkotaan .1381151 .0513342 2.69 0.007 .0375019 .2387283
gender
Laki-laki -.5201448 .0452454 -11.50 0.000 -.608824 -.4314655
_cons -22.07586 9.242128 -2.39 0.017 -40.1901 -3.961621
I'm currently writing a bachelor' thesis on determinant of demand for higher education. I have several independent variables, including ln expenditure per capita and ln expenditure per capita^2 to show diminishing marginal utility of educational expenditure. I have estimated the turning point of ln expenditure per capita^2 with: exp(-coefficient of the linear term/(2*coefficient of the squared term) and the result is =EXP(4.215897/(2*0.1161465)) = 76.213.474. This value does not lie within the range of data because the maximum value of expenditure per capita is 4.245.910.
Is it okay to have turning point that does not lie within the range of data? Or is it another way to estimate the turning point? And how to make a graph from quadratic function?
I would really appreciate any insight into my problem.
logit pt lncost lnopt_cost lnexpend_cap lnexpend_cap2 i.educhead i.socact i.lcc i.gender
Iteration 0: log likelihood = -7098.044
Iteration 1: log likelihood = -6208.2584
Iteration 2: log likelihood = -6166.0261
Iteration 3: log likelihood = -6165.5927
Iteration 4: log likelihood = -6165.5926
Logistic regression Number of obs = 12984
LR chi2(9) = 1864.90
Prob > chi2 = 0.0000
Log likelihood = -6165.5926 Pseudo R2 = 0.1314
pt Coef. Std. Err. z P>z [95% Conf. Interval]
lncost -.5694564 .0905392 -6.29 0.000 -.74691 -.3920029
lnopt_cost -.4964979 .0484262 -10.25 0.000 -.5914115 -.4015843
lnexpend_cap 4.215897 1.344818 3.13 0.002 1.580103 6.851692
lnexpend_cap2 -.1161465 .049625 -2.34 0.019 -.2134097 -.0188834
educhead
PT 1.674627 .080819 20.72 0.000 1.516224 1.833029
socact
Mengikuti Salah Satu K.. -.0138342 .0621084 -0.22 0.824 -.1355645 .1078962
Mengikuti Kedua Kegiat.. .10826 .057488 1.88 0.060 -.0044143 .2209343
lcc
Perkotaan .1381151 .0513342 2.69 0.007 .0375019 .2387283
gender
Laki-laki -.5201448 .0452454 -11.50 0.000 -.608824 -.4314655
_cons -22.07586 9.242128 -2.39 0.017 -40.1901 -3.961621
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