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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
Examples of grouped, simple and frequency distribution data
Importance of official statistic
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
Disadvantages For calculating median it is necessary to arrange the data; other averages do not need any arrangement. Since it is a positional average, its value is not d
Chebychev inequality
Standard Error The measure of reliability of the estimating equation that we have developed is given by standard error of estimate. The standard error of estimate represented b
The amounts of money won by the top ten finishers in a famous car race are listed below. $1,172,246 $163,659 $440,584 $350,634 $290,596 $186,731 $145,809 $143,2
(a) Average rainfall during the month of January is found to be 58 mm. A Class A pan evaporation recorded an average of 8.12 mm/day near an irrigation reservoir. The average
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
Type of Correlation 1. Positive and Negative Correlation: 2. Simple Partial and Multiple Correlations. 3. Linear and Non linear or Correlations
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