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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
Statistical Process Control The variability present in manufacturing process can either be eliminated completely or minimized to the extent possible. Eliminating the variabilit
If the sample size is less than 30, then we need to make the assumption that X (the volume of liquid in any cup) is normally distributed. This forces (the mean volume in the sam
Muti linear regression model problem An investigator is studying the relationship between weight (in pounds) and height (in inches) using data from a sample of 126 high school
The file Midterm Data.xls has a tab labeled "Income Data 2009". This data is collected income data from a sample of 400 people in 2009. Use a hypothesis test to see whether the av
Identify the (time, censor) pair for each of the following analyses:
Mode Mode is the value of the observation which occurs with the greatest frequency and thus it is the most fashionable value, Mode has been derived from French word La m
#questionMaximize Z= 3x1 + 2X2 Subject to the constraints: X1+ X2 = 4 X1 - X2 = 2 X1, X2 = 0..
Systematic Random Sampling This method is generally used in such cases where a complete list of the population is available from which sample has to be selected. Under this
Sequential Sampling Under this method, a number of sample lots are drawn one after another from a universe depending on the results of the earlier samples. Such sampling is gen
Two individuals, player 1 and player 2, are competing in an auction to obtain a valuable object. Each player bids in a sealed envelope, without knowing the bid of the other player
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