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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
A study was conducted to determine the amount of heat loss for a certain brand of thermal pane window. Three different windows were randomly subjected to each of three different ou
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How to a calculate the combined standard deviation for five groups (samples)?
The PCA is amongst the oldest of the multivariate statistical methods of data reduction. It is a technique for simplifying a dataset, by reducing multidimensional datasets to lower
Dr. Jim Mirabella UNIT EIGHT: DATA ANALYSIS PROJECT All Excel output should be copied into a single Word document where you must enter all of your responses to the questions below.
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
Pattie-Lynn's utility function for total assets is, in which A represents total assets in thousands of dollars. (a) Graph Pattie-Lynn's utility function. How would y
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Make a decision about the given claim. Use only the rare event rule, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coi
The project of building a backyard swimming pool consists of eight major activities and has to be completed within 19 weeks. The activities and related data are given in the follow
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