Feb26Response

Convolve the two 3x3 matrices that were assigned to you with your 9x9 matrix and calculate the resulting two matrices

Original Matrix

   [[ 0,  0, -1,  0,  0,  2,  1,  0, -1],
   [-1,  0,  0, -2, -1,  0, -1, -1, -1],
   [ 0,  0,  1,  1, -2,  0, -1, -1, -1],
   [-1,  1,  1,  0,  0,  1,  1,  1,  0],
   [-1,  1,  1, -2,  2,  2,  0,  1,  1],
   [-1,  0, -1, -1, -2,  1,  1,  1, -1],
   [ 0,  0,  1, -1, -1, -2,  1, -1,  0],
   [ 0, -1, -1,  2,  1, -1, -1,  0, -1],
   [ 1, -1,  1, -2,  2,  1, -1,  0, -1]] 9x9 matrix

Kernel1

   [[0, 0, 0],
   [0, 1, 1],
   [1, 0, 1]]
   3x3 matrix

Kernel1 convolved over matrix output

   [[ 1, -1, -4,  0, -4, -3, -4],
   [ 1,  3,  0, -1,  0,  0, -1],
   [ 2,  0,  3,  1,  4,  5,  2],
   [ 0, -2, -3,  4,  1,  3,  2],
   [ 0, -3, -3, -4,  2, -1,  1],
   [ 0,  1, -2, -2, -1, -1, -3],
   [ 0, -2,  6, -1, -1,  0, -3]]
   7x7 matrix

Kernel2

   [[0, 0, 1],
   [1, 1, 1],
   [1, 0, 0]]
   3x3 matrix

Kernel2 convolved over matrix output

   [[-2, -2, -2,  0, -3, -2, -5],
   [ 0,  1,  0, -1, -4, -2, -3],
   [ 1,  4,  0, -1,  3,  4,  1],
   [ 1,  0,  0,  2,  3,  5,  3],
   [-1, -4, -1, -1, -1,  2,  3],
   [ 0, -2, -4, -1,  0, -2, -2],
   [ 0, -2,  2, -2,  2, -2, -3]]
   7x7 matrix

What is the purpose of using a 3x3 filter to convolve across a 2D image matrix?

We use filters so that we can extract/preserve/highlight the features of the image that we deem important. Using filters on an image helps reduce processing times as well since the computer is only processing the features that are important.

Why would we include more than one filter? How many filters did you assign as part of your architecture when training a model to learn images of numbers from the mnist dataset?

You would include more than one filter to highlight multiple features of an image. Or maybe use one filter in conjunction with another with the idea that the first filter would highlight specific features that would then make it easier to highlight other features in the image. If I remember correctly we did not assign any filters on the mnist dataset.

MSE: From your 400+ observations of homes for sale, calculate the MSE for the following.

The 10 biggest over-predictions. The MSE for the 10 biggest overpredictions is 1,745,893,765,552.1667.

The 10 biggest under-predictions. The MSE for the 10 biggest underpredictions is 18,096,547,609,609.445.

The 10 most accurate results (use absolute value). The MSE for the 10 most accurate results is 46,568,555.92.

In which percentile do the 10 most accurate predictions reside? Did your model trend towards over or under predicting home values?

They resided between the 13th and 70th percentiles. My model predicted underpriced values for 187 homes and the rest out of the 400 were overpriced so my model slightly trends toward overpricing home values

Which feature appears to be the most significant predictor in the above cases?

Sqft seems to be the most significant predictor. After looking at a correlation matrix to see the correlation between price and the other variables it was revealed that price and sqft had the highest correlation of 0.52. Table below.

Stretch goal: calculate the MAE and compare with your MSE results

The MAE is 479052 and the MSE is 744,677,302,266.07 for all observations.