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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 consumer preference study involving three different bottle designs (A, B, and C) for the jumbo size of a new liquid detergent was carried out using a randomized block experimenta
The file Midterm Data.xls has a tab labeled "National Grid vs. Alcoa" which presents historical price data for two stocks. Using the National Grid price as the X-value and the Al
Sample Standard Deviation So far, we discussed the population standard deviation. Now, let us switch to sample standard deviation(s) that is analogous to the population stand
Related Positional Measures Besides median, there are other measures which divide a series into equal parts. Important amongst these are quartiles, deciles and percentiles.
X 110 120 130 120 140 135 155 160 165 155 Y 12 18 20 15 25 30 35 20 25 10
Assume that the normal distribution applies and find the critical z value(s). A = 0.04; H1 is mean ≠ 98.6 degrees Fahrenheit. Dteremine the value of Z. Find the value of the
(a) Average rainfall during the month of January is found to be 58 mm. A Class A pan evaporation recorded an average of 8.12 mm/day near an irrigation reservoir. The average
Geometric Mean is defined as the n th root of the product of numbers to be averaged. The geometric mean of numbers X 1 , X 2 , X 3 .....X n is given as
need help finding the n1 and s1 in the problem
Explanation of standard deviation and variance Describe the importance of standard deviation and variance, what they calculate and why they are required. Importance of char
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