3. Write the function stdev(values), that takes as a parameter a list of numbers, and calculates and returns the population standard deviation of the values in that list. The population standard deviation is the square-root of the population variance. For example: >>> X = [4,4,3,6,7] >>> stdev(x) 1.469693845669907 Notes: • Re-use your code! You should call your existing variance function from within stdev. This function does not require the accumulator pattern. These notes apply to problems 4 through 7. • The covariance, correlation, r-squared, and regression between two data sets requires that both data sets be of the same length. Use an assert statement to test for this condition and print out an error message if the lengths of the two lists are not the same. 4. Write the function covariance(x,y) that takes as parameters two lists of values, and calculates and returns the population covariance for those two lists. The population covariance is defined as: Oxy = {(x; -mx) [y: – My) i=1 For example: >>> X = [4,4,3,6,7] >>> y = [6,7,5,10,12] >>> covariance(x,y) 3.8 5. Write the function correlation(x,y) that takes as parameters two lists of values, and calculates and returns the correlation coefficient between these data series. The correlation coefficient is defined as: Pxy Oxy OxOy For example: >>> X = [4,4,3,6,7] >>> y = [6,7,5,10,12] >>> correlation(x,y) 0.9915217942181532 >>> correlation(list (range (10)), list(range (10,0,-1))) -0.9999999999999998
