this is the presentation of Statistic in which the topics of presentations were being told in a precise way to help the student

1. Presented to: Mr. Hafiz Fiyaz
Presented by: Group no. 9
Topic: (Principle of least square, Standard error of estimate,
Properties of least square, Regression line)

2. Principle of least square
• “The principle of least square consists of
determining the values of the values of the
unknown parameters that will minimize the
sum of squares of error”
• This concept was given by Karl F. Gauss (1777-
1855)

3. Continue…
• The basic formula of Principle of least square
by direct method is
• Y̑=a+bX+e
a= X²Y - xXY
nX² - (X)²
b= nXY – (X)(Y)
nX² - (X)²

4. Properties of least square
1. The least squares regression line always goes through the
point (X̅, Y̅) the mean of the data.
2. The sum of the deviations of the observed values of Y from
the least square regression line is always equal to zero i.e.
(Y- Y̑)=0
3. The sum of the squares of the derivations of the observed
values fro the least-squares regression line is a minimum i.e.
(Y- Y̑)² = minimum
4. The least square regression line obtained from a random
sample is the line of best fit because a and b are the
unbiased estimates of the parameters of α & β
5.

5. Standard error of Estimation
• the observed values of (X,Y) do not fall on the
regression line but they scatter away from it.
The degree of scatter or dispersion of the
observed values about the regression line is
measured by what is called standard error of
estimate.
• S=
•

6. Regression line
• A first step in finding a relationship between two variables
exists, is to plot each pair of independent-dependent
observation on graph paper using X-axis for regression
variable and Y-axis as dependent variable, this is called scatter
diagram. If a relationship between them exist then the point
show some sort of cluster around the line and these points
are called regression line
• Y= a + bX
α

7. Example