To test our hypothesis: Họ : Bị = Ba against H1 : B1 + Ba We first need to find the least squares estimates of the parameters. We will write our model as: y - X3 + e, e~ N(0, o².1) Then 3 = (X'X)-'(X'y) We also know that, MSE B~ N(3,0°(X'X)-'), Note that the degrees of freedom are n-5 because there are 5 parameters (%, 31,... , B5) that are estimated. .. B - Ba- N(31 – Ba, (s" + s* – 2s" J²) where s is the ()-ta element of (X'Xy!. and they are independent. ..T = n tn-5 under Ho VMSEVS" + 3 – 2s3 Using the above test statistic, we reject Ho at level of significance a if observed |t| > taçn-5
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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