execute the following line to import numpy and scipy



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import numpy as np
import scipy as sp
import scipy.optimize

Create a numpy array containing the numbers from 0 to 20

print the last value
print the last 4 values
print every second value



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Find indices of non-zero elements from [1,2,0,0,4,0]



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return all values greather or equal to 2 from [1,2,0,0,4,0]



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Create a null vector of size 10



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Create a vector containing 50 evenly spaced values between 0 and 2



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Construct a matrix by repeating the following row 5 times: [4, 0.2, 5.6, 1.2] (hint: np.repeat)



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Create a 4x4 identity matrix



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Create a 8x8 chessboard matrix (values 0 and 1)



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create a copy of the following matrix and set the first column to zeros. Check that the original matrix is ualtered



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Create a random vector of size 10 and sort it



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compute the mean of the random array



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find the smallest element of the random arary



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generate the follwing matrix (without explicitly writing it)

[[1, 6, 11],
[2, 7, 12],
[3, 8, 13],
[4, 9, 14],
[5, 10, 15]]



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compute the matrix product of two matrices of your choice



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compute the matrix product of the following matrices



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compute the determinant of the matrix product



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find the smallest element in matrix A



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use the matrix inverse function (np.linalg.inv) to solve the following linear equation system:

8 x + 2 y = 24
-4 x + y = -8



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compute the integral of the polynomial x^5 - 13x^3+ 3x^2



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search in the scipy library for a function to compute a zero-crossing (root) of the above polynomial



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Linear regression

We have a dataset which relates the final univerity grade of students to their high-school grades and grades from SAT tests^[1]. The dataset is given below and containts the following columns: 1. high school grade point average, 2. Math SAT score, 3. Verbal SAT score, 4. Computer science grade point average, 5. Overall university grade point average.

Compute a linear regression to predict the overall university grade point average from the remaining variables. Hint: the standard linear regression model reads:

$ y = X * \beta $

and the coefficients $\beta$ can be computed using the following formula:

$ \beta = (X^TX)^{-1}X^Ty $

compute the predicted values for the overall university grade ($y$) and the residuals ($y_i - data_i$). Compute the mean residual.

[1] source: http://onlinestatbook.com/2/case_studies/sat.html



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import pickle
import pylab
data = pickle.load(open('data.p', 'rb'))



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