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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
Root Mean Square Deviation The standard deviation is also called the ROOT MEAN SQUARE DEVIATION. This is because it is the ROOT (Step 4) of the MEAN (Step 3) o
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Caveat We must be careful when interpreting the meaning of association. Although two variables may be associated, this association does not imply that variation in the independ
This question explores the effect of estimation error on apparent arbitrage opportunities in a controlled simulation setting. We simulate returns for N = 10 assets over T = 30 year
Correlation The correlation is commonly used and a useful statistic used to describe the degree of the relationships between two or more variables. Pearson's correlation refle
In simple regression the dependent variable Y was assumed to be linearly related to a single variable X. In real life, however, we often find that a dependent variable may depend o
a) What is meant by secular trend? Discuss any two methods of isolating trend values in a time series.
The following dataset is from a study of the effects of second hand smoking in Baltimore, MD, and Washington, DC. For the 25 children involved in this study the outcome variable is
The data in the data frame compensation are from Myers (1990), Classical andModern Regression with Applications (Second Edition)," Duxbury. The response y here is executive compens
To determine the proportion of people in your town who are smokers, it has been decided to poll people at one of the following local spots: (a) the pool hall; (b) the bowling alley
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