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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
Use only the rare event rule, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coin favors heads and sample results consis
A researcher is interested in comparing the effectiveness of three different parts of therapy for anger problems. 8 participants are randomly assigned to 3 treatment conditions: Co
Chi-square analysis can be used with both Goodness-of-Fit Tests and with Tests for Independence. There are specific instances when each test should be used based on the information
Agreement The degree to which different observers, raters or diagnostic the tests agree on the binary classification. Measures of agreement like that of the kappa coefficient qu
Sampling A Population is a collection of all the data points being studied. For example, if we are studying the annual incomes of all the people in India, then the population
Measurement of trend , least square method
A) The three images shown below were blurred using square masks of sizes n=23, 25, and 45, respectively. The vertical bars on the le_ lower part of (a) and (c) are blurred, but a c
From the information given, what seems to be the main flaw in each of the following statistical generalisations? (i) Banking industry employees are facing a crisis, if their
(a) Elevation (m) 0 400 800 1200 1600 2000 2400 2800 3200 4000 480
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
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