A Mathematical Tool for Inference in Logistic Regression with Small-Sized Data Sets: A Practical Application on ISW-Ridge Relationships

<table class="table-group" id="tab6"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td align="center" colspan="2">Point</td><td align="center">95% Wald</td></tr><tr class="thead"><td align="left">Effect</td><td align="center">Estimate</td><td align="center">Confidence limits</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td align="left"><span style="width: 19.924999px;"><svg height="15.25" id="M92" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 19.924999 15.25" width="19.924999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M775 650l-6 -28q-60 -6 -81.5 -16t-61.5 -54l-175 -191l125 -243q30 -58 48.5 -71t82.5 -19l-5 -28h-275l7 28l35 4q31 4 37 12t-6 34l-108 216q-140 -165 -177 -219q-16 -22 -10.5 -30.5t41.5 -13.5l22 -3l-7 -28h-244l8 28q52 4 75 15.5t67 52.5q48 46 206 231
l-110 215q-26 51 -44 63t-72 17l6 28h250l-6 -28l-27 -4q-30 -5 -35 -10t3 -27q17 -43 95 -190q70 78 154 185q15 21 10 29.5t-33 12.5l-30 4l5 28h236z" id="x1D44B"></path></g>
<g transform="matrix(.012,-0,0,-.012,13.525,15.187)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg></span></td><td align="center">0.453</td><td align="center">0.247 <svg height="5.7375002" id="M93" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 10.1 5.7375002" width="10.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,5.675)"><path d="M548 311q-21 -57 -59 -94t-89 -37q-53 0 -128 52q-55 38 -84 38q-39 0 -70.5 -23t-45.5 -60l-32 12q21 57 59 94t89 37q53 0 128 -52q55 -38 84 -38q39 0 70.5 23t45.5 60z" id="x223C"></path></g>
</svg> 0.832</td></tr><tr><td align="left"><span style="width: 19.924999px;"><svg height="15.25" id="M94" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 19.924999 15.25" width="19.924999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M775 650l-6 -28q-60 -6 -81.5 -16t-61.5 -54l-175 -191l125 -243q30 -58 48.5 -71t82.5 -19l-5 -28h-275l7 28l35 4q31 4 37 12t-6 34l-108 216q-140 -165 -177 -219q-16 -22 -10.5 -30.5t41.5 -13.5l22 -3l-7 -28h-244l8 28q52 4 75 15.5t67 52.5q48 46 206 231
l-110 215q-26 51 -44 63t-72 17l6 28h250l-6 -28l-27 -4q-30 -5 -35 -10t3 -27q17 -43 95 -190q70 78 154 185q15 21 10 29.5t-33 12.5l-30 4l5 28h236z" id="x1D44B"></path></g>
<g transform="matrix(.012,-0,0,-.012,13.525,15.187)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg></span></td><td align="center">3.056</td><td align="center">1.393 <svg height="5.7375002" id="M95" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 10.1 5.7375002" width="10.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,5.675)"><path d="M548 311q-21 -57 -59 -94t-89 -37q-53 0 -128 52q-55 38 -84 38q-39 0 -70.5 -23t-45.5 -60l-32 12q21 57 59 94t89 37q53 0 128 -52q55 -38 84 -38q39 0 70.5 23t45.5 60z" id="x223C"></path></g>
</svg> 6.703</td></tr><tr><td align="left"><span style="width: 19.924999px;"><svg height="15.4" id="M96" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 19.924999 15.4" width="19.924999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M775 650l-6 -28q-60 -6 -81.5 -16t-61.5 -54l-175 -191l125 -243q30 -58 48.5 -71t82.5 -19l-5 -28h-275l7 28l35 4q31 4 37 12t-6 34l-108 216q-140 -165 -177 -219q-16 -22 -10.5 -30.5t41.5 -13.5l22 -3l-7 -28h-244l8 28q52 4 75 15.5t67 52.5q48 46 206 231
l-110 215q-26 51 -44 63t-72 17l6 28h250l-6 -28l-27 -4q-30 -5 -35 -10t3 -27q17 -43 95 -190q70 78 154 185q15 21 10 29.5t-33 12.5l-30 4l5 28h236z" id="x1D44B"></path></g>
<g transform="matrix(.012,-0,0,-.012,13.525,15.187)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" id="x33"></path></g>
</svg></span></td><td align="center">0.486</td><td align="center">0.289 <svg height="5.7375002" id="M97" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 10.1 5.7375002" width="10.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,5.675)"><path d="M548 311q-21 -57 -59 -94t-89 -37q-53 0 -128 52q-55 38 -84 38q-39 0 -70.5 -23t-45.5 -60l-32 12q21 57 59 94t89 37q53 0 128 -52q55 -38 84 -38q39 0 70.5 23t45.5 60z" id="x223C"></path></g>
</svg> 0.819</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab6

Table 6

Table 6: A Mathematical Tool for Inference in Logistic Regression with Small-Sized Data Sets: A Practical Application on ISW-Ridge Relationships 