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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
Active Control Equivalence Studies (ACES) Clinical trials the field in which the object is easy to show that the new treatment is as good as the existing treatment. Such type
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Simulation When decisions are to be taken under conditions of uncertainty, simulation can be used. Simulation as a quantitative method requires the setting up of a mathematical
Canonical correlation analysis (CC) allows the investigation of the relationship between two ,sets of variables. For example, a sociologist may want to investigate the Relationship
Systematic Sampling In Systematic Sampling each element has an equal chance of being selected, but each sample does not have the same chance of being selected. Here,
Sampling Error It is the difference between the value of the actual population parameter and the sample statistic. Samples are used to arrive at conclusions regarding the p
Grouped data For grouped data, the formula applied is σ = Where f = frequency of the variable, μ= population mea
10. If a set of scores has a sample mean of 25 and a sample variance of 4, find the following: a. the z-score for a raw score of 31 b. the z-score for a raw score of 18 c. the raw
Steps in ANOVA The three steps which constitute the analysis of variance are as follows: To determine an estimate of the population variance from the variance that exi
Examples of grouped, simple and frequency distribution data
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