1. What is the classification accuracy for the new neural network you just built? Provide the complete formula used (i.e. show your work) along with the final percentage (rounded to two decimals places).

3. Neural Network - Running the Method:
4. Run set.seed(12345) and then run the neuralnet() function to build the network storing the results in a variable called nn with 2 hidden layers and setting linear.output to TRUE. Include the command and discuss the input parameters you used. WARNING: When building your neural network, you may notice that it takes a long time to build or periodically may error out with a failure to converge. If this happens, simply run the command again until it works.

library(neuralnet)

## Warning: package 'neuralnet' was built under R version 3.5.2

#Defining formula

set.seed(12345)

nn = neuralnet(class ~ pelvic_incidence + pelvic_tilt + lumbar_lordosis + sacral_slope + pelvic_radius + degree_spondylolisthesis, scaledvertdat, hidden=2,linear.output=TRUE)

DIscusion

The model converged easily because the data was normalized. The specifications of the model allowed for the creation of of model with 2 hidden layers with a linear output. There are two nuerons for each hidden layer in the neural network.

2. Run the command nn$result.matrix. Include the output screenshot and answer the following questions:

nn$result.matrix

## [,1]

## error 14.20819370

## reached.threshold 0.00999483

## steps 1567.00000000

## Intercept.to.1layhid1 2.37067931

## pelvic_incidence.to.1layhid1 0.53727495

## pelvic_tilt.to.1layhid1 -0.55824245

## lumbar_lordosis.to.1layhid1 -1.88777999

## sacral_slope.to.1layhid1 0.68130772

## pelvic_radius.to.1layhid1 -0.79312436

## degree_spondylolisthesis.to.1layhid1 12.19635106

## Intercept.to.1layhid2 -4.68484036

## pelvic_incidence.to.1layhid2 4.05981734

## pelvic_tilt.to.1layhid2 -8.37622977

## lumbar_lordosis.to.1layhid2 -1.24504474

## sacral_slope.to.1layhid2 13.07119591

## pelvic_radius.to.1layhid2 12.37203090

## degree_spondylolisthesis.to.1layhid2 -75.48984472

## Intercept.to.class -0.49324621

## 1layhid1.to.class 1.55493315

## 1layhid2.to.class -0.87186029

How many steps were needed to build your neural network?

1567 steps