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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
PROPERTIES 1. The value of standard deviation remains the same if, in a series each of the observation is increased or decreased by a constant quantity. In statistical lan
The following are the various types of common averages used in statistical analysis given in the form of a chart. Figure 1
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Chebychev inequality
In simple regression the dependent variable Y was assumed to be linearly related to a single variable X. In real life, however, we often find that a dependent variable may depend o
Determine the maximum weight in kN to one decimal point (1 DP) of the engine that can be supported without exceeding the tension given in Parameter 1 (P1) in chain AB or 1.1 x P1
The weight of the engine in kN is given in P2 and is suspended from a vertical chain at A. A second chain round the engine is attached at A, with a spreader bar between B and C. Th
Mean Absolute Deviation To avoid the problem of positive and negative deviations canceling out each other, we can use the Mean Absolute Deviation which is given by
Suppose that before the minimum wage law change, the underlying mean number of part-time employees per Burger King Restaurant in New Jersey was 20.3. It was thought that the increa
Properties of correlation
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