2 Y; = 706 2 XiYi = 209,952 2 X² = 1,336,749 > Y² = 33,106 %3D %3D %3D i=1 i=1 i=1 i=1 A. Calculate X and Y 4478 706 ti9tI B. Calculate s C. Calculate Bo and Bi 179.12 25 28.24 222,527.L S401 104 Denoting the residuals from the estimated regression model by û,, show that the sum of the residuals equals zera 25, 2. L Σ-0 %3D i=1 Cxi-7)² Show that: Y = + û, Bo+B,X, %3D %3D is equivalent to: У; B,x, + û, where y, = Y-Y and x, Y,-Y and x, = X, - X %3D %3D %3D 4. Consider the estimated simple linear regression model Y, = B + B, X, + û, . Show that the estimated conditi %3D mean function fits through the sample means of the data. That is, show that Y = Y if X= X . %3D 5. Derive the least-squares estimators of the intercept ( B,) and slope (B) for the simple linear regression moc Show all steps for credit. 3.

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Q: part c parked as wrong answer

A: Mean()=12Standard deviation()=4

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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.