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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
Advantages of Sampling Why should we settle on a sample instead of studying the entire population? Sampling has the following advantages over a census (study of the entire pop
#question what is the statistical process to reduce hardness of water
Exercise: (Binomial and Continuous Model.) Consider a binomial model of a risky asset with the parameters r = 0:06, u = 0:059, d = 0:0562, S0 = 100, T = 1, 4t = 1=12. Note that u
Disadvantages The value of mode cannot always be determined. In some cases we may have a bimodal series. It is not capable of algebraic manipulations. For example, from t
Comparison of the Principal Averages-Mean, Median and Mode The mean, median, and mode are located at the same point in a symmetrical frequency distri
calculate variance and standard deviation of the following sample 12,22,32,13,12,23,34,52,56,23,44,32,11,11
Stratified Sampling Stratified Sampling is generally used when the population is heterogeneous. In this case, the population is first subdivided into several parts (or s
To use Linear Programming for solving the following inequalities. Following Twin Conditions (as mandated by the Indian Regulatory Authority) Twin Condition I for TV Broadcasters
Muti linear regression model problem An investigator is studying the relationship between weight (in pounds) and height (in inches) using data from a sample of 126 high school
a) What is meant by secular trend? Discuss any two methods of isolating trend values in a time series.
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