Write a Python function that takes as inputs a vector of values and returns a vector of semivariances, which we will define as the Euclidean distance between each pair of observations: , where x_i and x_j represent different values. Your code should compute and return the semivariance as a vector, with no repetitions (i.e., you can't just use a simple double for-loop because ). There are several possible ways to solve the problem, including a modified double for-loop, or write a separate function.

Use Python.   Q1. Suppose deg is an angle in degrees.  Write down the NumPy code that computes the counterclockwise rotation matrix.  Don't forget to convert the angles into radians when necessary.   def rotate(deg):   Q2. Let x be a vector.  How do you use rotate(deg) to find a vector y that is normal to x?  Namely <x,y> = 0.   y = ...   Q3. Let x be a vector.  How do you find a vector v in the same direction as x but with |v| = 1.   v = ...   Q4. A hyperplane in 2D is the same as a line.  A hyperplane is defined by a normal vector w and a bias scalar b.  Write down the expression that defines points on the line that is the hyperplane in 2D defined by (w, b).   { x : ... }   Q5. Given a vector x, and a hyperplane P defined by (w, b).  Describe how to compute the point v that is the projection of x on to the plane P.

Write a python function sqr(n) that returns the square of its parameter n for example: Test Result print(sqr(-3)) 9 print(sqr(11)) 121

In Python, write a function that produces plots of statistical power versus sample size for simple linear regression. The function should be of the form LinRegPower(N,B,A,sd,nrep), where N is a vector/list of sample sizes, B is the true slope, A is the true intercept, sd is the true standard deviation of the residuals, and nrep is the number of simulation replicates. The function should conduct simulations and then produce a plot of statistical power versus the sample sizes in N for the hypothesis test of whether the slope is different than zero. B and A can be vectors/lists of equal length. In this case, the plot should have separate lines for each pair of A and B values (A[1] with B[1], A[2] with B[2], etc). The function should produce an informative error message if A and B are not the same length. It should also give an informative error message if N only has a single value. Demonstrate your function with some sample plots. Find some cases where power varies from close to zero to…