diff --git a/14_stats_and_montecarlo/octave-workspace b/14_stats_and_montecarlo/octave-workspace index 41ef164..8c437bb 100644 Binary files a/14_stats_and_montecarlo/octave-workspace and b/14_stats_and_montecarlo/octave-workspace differ diff --git a/16_splines/octave-workspace b/16_splines/octave-workspace index 8c437bb..65972c0 100644 Binary files a/16_splines/octave-workspace and b/16_splines/octave-workspace differ diff --git a/17_integrals_and_derivatives/octave-workspace b/17_integrals_and_derivatives/octave-workspace index 8c437bb..1af79bd 100644 Binary files a/17_integrals_and_derivatives/octave-workspace and b/17_integrals_and_derivatives/octave-workspace differ diff --git a/extra_credit/.README.md.swp b/extra_credit/.README.md.swp new file mode 100644 index 0000000..6adbb81 Binary files /dev/null and b/extra_credit/.README.md.swp differ diff --git a/extra_credit/README.md b/extra_credit/README.md index 1234d6d..1e348f0 100644 --- a/extra_credit/README.md +++ b/extra_credit/README.md @@ -27,22 +27,21 @@ columns with your netid on each row as such, **Nonlinear Regression - Logistic Regression** -![logistic regression of Challenger O-ring failure](http://www.stat.ufl.edu/~winner/cases/challenger.ppt) +[logistic regression of Challenger O-ring failure](http://www.stat.ufl.edu/~winner/cases/challenger.ppt) Use the Temperature and failure data from the Challenger O-rings [challenger_oring.csv](./challenger_oring.csv). Your independent variable is temperature and your dependent variable is failure (1=fail, 0=pass). Create a function called `cost_logistic.m` that takes the vector `a`, and independent variable `x` and dependent variable `y`. Use the -function, $\sigma(t)=\frac{1}{1+e^{-t}}$ where $t=a_{0}+a_{1}x$. Use the cost function, +function, ![sigma](./equations/sigma.png) where ![t](./equations/t.png). Use the cost function, -$J(a_{0},a_{1})=1/m\sum_{i=1}^{n}\left[-y_{i}\log(\sigma(t_{i}))-(1-y_{i})\log((1-\sigma(t_{i})))\right]$ +![cost](./equations/cost.png) and gradient -$\frac{\partial J}{\partial a_{i}}= -1/m\sum_{k=1}^{N}\left(\sigma(t_{k})-y_{k}\right)x_{k}^{i}$ +![costgrad](./equations/costgrad.png) -where $x_{k}^{i} is the k-th value of temperature raised to the i-th power (0, and 1) +where ![x](./equations/x.png) is the k-th value of temperature raised to the i-th power (0, and 1) a. edit `cost_logistic.m` so that the output is `[J,grad]` or [cost, gradient] diff --git a/extra_credit/equations/.cost.tex.swp b/extra_credit/equations/.cost.tex.swp new file mode 100644 index 0000000..39760ef Binary files /dev/null and b/extra_credit/equations/.cost.tex.swp differ diff --git a/extra_credit/equations/.costgrad.tex.swp b/extra_credit/equations/.costgrad.tex.swp new file mode 100644 index 0000000..8af489c Binary files /dev/null and b/extra_credit/equations/.costgrad.tex.swp differ diff --git a/extra_credit/equations/.sigma.tex.swp b/extra_credit/equations/.sigma.tex.swp new file mode 100644 index 0000000..9ce1665 Binary files /dev/null and b/extra_credit/equations/.sigma.tex.swp differ diff --git a/extra_credit/equations/.t.tex.swp b/extra_credit/equations/.t.tex.swp new file mode 100644 index 0000000..b05831e Binary files /dev/null and b/extra_credit/equations/.t.tex.swp differ diff --git a/extra_credit/equations/.x.tex.swp b/extra_credit/equations/.x.tex.swp new file mode 100644 index 0000000..f2e0039 Binary files /dev/null and b/extra_credit/equations/.x.tex.swp differ diff --git a/extra_credit/equations/cost.png b/extra_credit/equations/cost.png new file mode 100644 index 0000000..c1092a7 Binary files /dev/null and b/extra_credit/equations/cost.png differ diff --git a/extra_credit/equations/cost.tex b/extra_credit/equations/cost.tex new file mode 100644 index 0000000..0a5d023 --- /dev/null +++ b/extra_credit/equations/cost.tex @@ -0,0 +1,2 @@ +J(a_{0},a_{1})=1/m\sum_{i=1}^{n}\left[-y_{i}\log(\sigma(t_{i}))-(1-y_{i})\log((1-\sigma(t_{i})))\right] + diff --git a/extra_credit/equations/costgrad.png b/extra_credit/equations/costgrad.png new file mode 100644 index 0000000..15eb272 Binary files /dev/null and b/extra_credit/equations/costgrad.png differ diff --git a/extra_credit/equations/costgrad.tex b/extra_credit/equations/costgrad.tex new file mode 100644 index 0000000..5537f3d --- /dev/null +++ b/extra_credit/equations/costgrad.tex @@ -0,0 +1,2 @@ +\frac{\partial J}{\partial a_{i}}=1/m\sum_{k=1}^{N}\left(\sigma(t_{k})-y_{k}\right)x_{k}^{i} + diff --git a/extra_credit/equations/sigma.png b/extra_credit/equations/sigma.png new file mode 100644 index 0000000..ca351f1 Binary files /dev/null and b/extra_credit/equations/sigma.png differ diff --git a/extra_credit/equations/sigma.tex b/extra_credit/equations/sigma.tex new file mode 100644 index 0000000..3d909e5 --- /dev/null +++ b/extra_credit/equations/sigma.tex @@ -0,0 +1,2 @@ +\sigma(t)=\frac{1}{1+e^{-t}} + diff --git a/extra_credit/equations/t.png b/extra_credit/equations/t.png new file mode 100644 index 0000000..2aad89f Binary files /dev/null and b/extra_credit/equations/t.png differ diff --git a/extra_credit/equations/t.tex b/extra_credit/equations/t.tex new file mode 100644 index 0000000..934ed58 --- /dev/null +++ b/extra_credit/equations/t.tex @@ -0,0 +1 @@ +t=a_{0}+a_{1}x diff --git a/extra_credit/equations/x.png b/extra_credit/equations/x.png new file mode 100644 index 0000000..6394239 Binary files /dev/null and b/extra_credit/equations/x.png differ diff --git a/extra_credit/equations/x.tex b/extra_credit/equations/x.tex new file mode 100644 index 0000000..5432d99 --- /dev/null +++ b/extra_credit/equations/x.tex @@ -0,0 +1 @@ +x_{k}^{i}