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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
Angle Count method The method for estimating the proportion of the area of a forest which is in fact covered by the bases of trees. An observer goes to each of the number of po
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
Construct index numbers of price for the following data by applying: i) Laspeyre’s method ii) Paasche’s method iii) Fisher’s Ideal Index number
(1) Assume we categorize voters in a city as havingless educationand those havingmoreeducation. Those with less education have less than a college degree; those with more education
difference between large sample test and small sample test
Origin and Development of probability Theory: The credit for origin and development of probability goes to the European gamblers of 17 th century. They used to gamble on gam
A researcher computed the F ratio for a four-group experiment. The computed F is 4.86. The degrees of freedom are 3 for the numerator and 16 for the denominator. 1. Is the computed
Jocko's Garage has been accused of insurance fraud. Data on estimates made by Jocko and another garage were obtained for 10 damaged vehicles (available in 'jockogarage.txt'). Here
Geometric Mean The geometric mean of numbers is defined as the th root of the product of numbers .It is obtained by multiplying all the values of a variable and then extracti
Chebychev inequality
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