For fun: download a workplace friendly image/photo, or use one you have already (jpg or png format should be fine). Use matplotlib to convert the image to a float point array. (If you have a color image, average the the [RGB] colors together.) Write the array to a new image file (jpg or png) and save it. Check that you recover the original image, or at least a black-n-white version of it. [I used imread/imsave.] Treating the image as a matrix, perform SVD on it (A=U.S.Vt). Note the values in the diagonal elements of the S array. See how many you can zero out without degrading the image quality. (This is an example of image compresshion....)
In this exercise, generate mock data for this function
y = (0.5-x)*(1.5+x)*(1-x)+noisewhere "noise" is a normal deviate with mu=0 and s.d.=0.5. Choose n=15 samples in x, evenly spaced in the interval [-2,+2]. Fit the mock data with
For the mock data in the previous exercise, fitted with your favorite method (other than bootstrap, which of course is everyone's real favorite), estimate a p-value for your fit. Try using an unrealistically small value for the error in your fit, and again with a lartge value. How does the p-value change?