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The regression line should be drawn on the scatter diagram in such a way that when the squared values of the vertical distance from each plotted point to the line are added, the total amount will be the smallest possible amount. This criterion is called the Method of Least Squares.
Minimizing the sum of the squared differences of each value of Y from the regression line by the method of calculus, we arrive at two equations, called the normal equations:
Solving these equations simultaneously, and using equivalent expressions for and , we obtain the following formulae used to calculate the coefficients a and b in the regression line = = a + bX
E(Y|X = x) = a + bx
Sample Standard Deviation So far, we discussed the population standard deviation. Now, let us switch to sample standard deviation(s) that is analogous to the population stand
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1 A penny is tossed 5 times. a. Find the chance that the 5th toss is a head b. Find the chance that the 5th toss is a head, given the first 4 are tails.
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In New Jersey, banks have been charged with withdrawing from counties having a high percentage of minorities. To substantiate this charge, data is presented in the table below conc
Find the minimum constant workforce: ABC Company, a manufacturer of roofing supplies, has developed monthly forecasts for roofing tiles. The forecasted demand and the expected
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