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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
Assume that the pulley at A is a small frictionless pulley. The cord AB is only allowed to support a maximum tension in Newtons as given in P4, and the cord supporting the block ca
Estimate the standard deviation of the process: Draw the X (bar) and R charts for the data given and give your comments about the process under study. Estimate the standard de
Given a certain population there are various ways in which a sample may be drawn from it. The chart below illustrates this point: Figure 1 In Judgem
Of the 6,325 kindergarten students who participated in the study, almost half or 3,052 were eligible for a free lunch program. The categorical variable sesk (1 == free lunch, 2 = n
Coefficient of Variation The standard deviation discussed above is an absolute measure of dispersion. The corresponding relative measure is known as the coefficient of vari
Variance The term variance was used to describe the square of the standard deviation by R.A.Fisher. The concept of variance is highly important in areas where it is possible to
1. For each of the following variables: major, graduate GPA, and height: a. Determine whether the variable is categorical or numerical. b. If the variable is numerical, deter
Cluster Sampling This method is also known as multi stage sampling .Under this method random selection is made of the ultimate or final units from a given stratum. The sampling
Characteristics of Index Number On the analysis of various definitions of index number the following may be its characteristics: 1. Expressed in Number : Index number
Based on the following graphs (next page) you should write a discussion report (2 pages) on: 1. Determination of whether the open-loop system response is consistent with a 1st o
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