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How do you calculate degrees of freedom for a correlation?
To calculate the degrees of freedom for a correlation, you have to subtract 2 from the total number of pairs of observations. If we denote degrees of freedom by df, and the total number of pairs of observations by N, then: Degrees of freedom, df=N-2. For instance, if you observed height and weight in 100 subjects, you have 100 pairs of observations since each observation of height and weight constitutes one pair. If you want to calcualte the correlation for these two variables (height and weight), your degrees of freedom would be calculated as follows: N=100 df=N-2 Therefore, df=100-2=98 The degrees of freedom are a function of the parameters; you subtract the amount of parameters free to vary from the n to get the df, so logically in a correlation we should subtract 2 from n, as we are looking at a correlation between 2 variables.
Are there non-singular skew-symmetric n n matrices with odd n?
No, there cannot be any.
How many pairs of twin prime numbers are there between 1 and 100?
Eight pairs. Two prime numbers M and N are twin primes if |M-N| = 2. So here are the list of prime numbers less than 100:2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.There are 8 pairs of twin primes here:3,55,711,1317,1929,3141,4359,6171,73
What is 100 percent when 30 percent is 27?
90 is the 100%.100% :N = 30% : 2730%N = 27 (100%)N = 27(100%)/30%N = 2700/30N = 90
Show that a full parenthesization of an n-element expression has exactly n-1 pairs of parentheses?
A pair of parentheses musts contain a operator and n elements must have n-1 operators, so a full parenthesization of an n-element expression has exactly n-1 pairs of parentheses.
