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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
Median Median is a position average. It is the value of middle item of a variable when the items are arranged according to their values either in ascending or descending order.
Estimate a linear probability model: Consider the multiple regression model: y = β 0 +β 1 x 1 +.....+β k x k +u Suppose that assumptions MLR.1-MLR4 hold, but not assump
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construction of control chart,n chart
Examples of grouped, simple and frequency distribution data
The total number of overtime hours (in 1000s) worked in a large steel mill was recorded for 16 quarters, as shown below. Year Quarter Overtime hour
You will recall the function pnorm() from lectures. Using this, or otherwise, Dteremine the probability of a standard Gaussian random variable exceeding 1.3. Using table(), or
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
how can we use measurement error method with eight responses variables (we do not have explanatory variable in the data )?.the data analyse 521 leaves ..
If the economy does well, the investor's wealth is 2 and if the economy does poorly the investor's wealth is 1. Both outcomes are equally likely. The investor is offered to invest
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