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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
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In the early 1990s researchers at The Ohio State University studied consumer ratings of six fast-food restaurants: Borden Burger, Hardee's, Burger King, McDonald's, Wendy's, and Wh
Lorenz Curve It is a graphic method of measuring dispersion. This curve was devised by Dr. Max o Lorenz a famous statistician. He used this technique for wealth it i
The box plot displays the diversity of data for the income; the data ranges from 20 being the minimum value and 1110 being the maximum value. The box plot is positively skewed at 4
(1) What values can the response variable Y take in logistic regression, and hence what statistical distribution does Y follow? The response variable can take the value of either
This probability rule determined by the research of the two mathematicians Bienayme' and Chebyshev, explains the variability of data about its mean when the distribution of the dat
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Ask 3. Precision Manufacturing has a government contract to produce stainless steel rods for use in military aircraft. Each rod is required to be 20 millimeters in diameter. Each
You have an assembly line which produces 1L bottles of seltzer with a standard deviation of 0.05L. • Assuming the distribution of volume is normal, what is the chance any single
As we stated above, we start factor analysis with principal component analysis, but we quickly diverge as we apply the a priori knowledge we brought to the problem. This knowled
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