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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
programming
(a) At a stream gauging station, the following discharges and stage measurements were taken for the purpose of the rating curve at that section: Stage (m) 1
Importance and Application of probability: Importance of probability theory is in all those areas where event are not certain to take place as same as starting with games of
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
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
Lifts usually have signs indicating their maximum capacity. Consider a sign in a lift that reads "maximum capacity 1400kg or 20 persons". Suppose that the weights of lift-users are
X 110 120 130 120 140 135 155 160 165 155 Y 12 18 20 15 25 30 35 20 25 10
In reduced rank regression (RRR), the dependent variables are first submitted to a PCA and the scores of the units are then used as dependent variables in a series of
the two regrassion line will pass through the point (x,y)
Skewness Meaning and Definition Literal meaning of skewness is lack of symmetry; it is a numerical measure which reveals asymmetry of a statistical series. According t
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