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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
Analysis of covariance (ANCOVA) It is initially used for an expansion of the analysis of variance which permits to the possible effects of continuous concomitant variables (suc
There are 15 types of ice cream: A,B,C,D,E,F,G,H,I,J,K,L,M,N, and O. How many combinations are there to sample 5 flavors if you sample 1 flavor 4 times? How many combinations are t
Multi stage or Cluster Random sampling Under this method, the random selection is made of primary, intermediate and final units from a given population. The area of investigat
The Null Hypothesis - H0: The random errors will be normally distributed The Alternative Hypothesis - H1: The random errors are not normally distributed Reject H0: when P-v
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
Choose any published database from the internet or Bethel library (such as those from the Census Bureau or any financial sites). You may opt to use one of the data files provided b
Suppose that in the actual survey of 50 prospective customers, 6 subscribe to the 3 for all offer, what does this tell you about the previous estimate of the proportion of customer
it is said that management is equivalent to decision making? do you agree? explain
Statistics Can Lead to Errors The use of statistics can often lead to wrong conclusions or wrong estimates. For example, we may want to find out the average savings by i
Assumptions in Regression To understand the properties underlying the regression line, let us go back to the example of model exam and main exam. Now we can find an estimate o
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