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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
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
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There may be two values which occur with the same maximum frequency. The distribution is then called bimodal. In a bimodal distribution, the value of mode cannot be determined with
Statistical Process Control The variability present in manufacturing process can either be eliminated completely or minimized to the extent possible. Eliminating the variabilit
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To study the physical fitness of a sample of 28 people, the data below was collected representing the number of sit-ups that a person could do in one minute. 10 12
In an agricultural experiment, we wish to compare the yields of three different varieties of wheat. Call these varieties A, B and C. We have a ?eld that has been marked into a 3 *
Prediction Inte rval We would like to construct a prediction interval around which would contain the actual Y. If n ≥ 30, ± Zs e would be the interval, where Z
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
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