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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 Case Study included information about the price for a full meal before and after the law change (in dollars). Of interest is whether the differences in price for a full meal b
Other Measures of Dispersion In this section, we look at relatively less used measures of dispersion like fractiles, deciles, percentiles, quartiles, interquartile range and f
Related Positional Measures Besides median, there are other measures which divide a series into equal parts. Important amongst these are quartiles, deciles and percentiles.
in a normal distribution with a mean of 85 and a STD of 5, what is the percentage of scores between 75 and 90?
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Mode Mode is the value of the observation which occurs with the greatest frequency and thus it is the most fashionable value, Mode has been derived from French word La m
Circles or Pie Diagram: Circles or pie diagrams are alternative to squares. These are used for the same purpose i.e. when the values are differing widely in their magnitude
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Bernoulli's Theorem If a trial of an experiment can result in success with probability p and failure with probability q (i.e.1-p) the probability of exactly r success in n tri
Agreement The degree to which different observers, raters or diagnostic the tests agree on the binary classification. Measures of agreement like that of the kappa coefficient qu
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