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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
To study the physical fitness of a sample of 28 people, the data below was collected representing the number of sit-ups that a person could do in one minute. 10 12
the two regrassion line will pass through the point (x,y)
Each section of the SAT test is supposed to be distributed normally with a mean of 500 and a standard deviation of 100. Suppose 5 students in a class took the SAT math test. They r
Calculation of Degrees of Freedom First we look at how to calculate the number of DOF for the numerator. In the numerator since we calculate the variance from the sample means,
in a normal distribution with a mean of 85 and a STD of 5, what is the percentage of scores between 75 and 90?
how to write result in the end of price index number problem
The mean tax-return preparation fee H&R Block charged retail customers in 2012 was $183 (The Wall Street Journal, March 7, 2012). Use this price as the population mean and assume t
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
The median, as the name suggests, is the middle value of a series arranged in any of the orders of magnitude i.e. ascending or descending order. As distinct from the arithmetic
simplified formulae
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