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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
Consider the sample of 60 package design ratings given in the table below. A Sample of Package Design Ratings (Composite S
history of north west corner method
1. Calculate the mean and mode of: Central size 15 25 35 45 55 65 75 85 Frequencies 5 9 13 21 20 15 8 3 The following data shows the monthly expenditure of 80 students of
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Let X, Y, and Z refer to the three random variables. It is known that Var(X) = 4, Var(Y) = 9, and Var(Z) = 16. It is further known that E(X) = 1, E(Y) = 2, and E(Z) = 4. Furthermor
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1) Suppose you want to test a hypothesis that two treatments, A and B, are equivalent against the alternative that the response for A tend to be larger than those of B. You plan to
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applications of normal probability distribution
Evaluate Gross Reproduction Rate: From the data given below compute : i) General Fertility Rate ii) Specific Fertility Rate iii) Total Fertility Rate iv)
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