Page 13 - Industrial Process Plant Construction Estimating and Man Hour Analysis

xxviii Introduction

Chart Elements: Axes, Axis Titles, Chart Title, Gridlines, Data Table.

Frequency distribution
Bin Frequency
0.11 1
0.12 2
0.30 1
0.49 1
0.60 2
More 1

Regression analysis and correlation
Method of least squares

Linear regression: Fitting a straight line
The straight-line relationship can be valuable in summarizing the observed
dependence of one variable on another. The most common type of linear regres-
sion is called ordinary least-squares regression. Linear regression uses the
values from an existing data set consisting of measurements of the values of
two variables, x and y, to develop a model that is useful for predicting the value
of the dependent variable, y for given values of x. Thus, the statistical tech-
niques used in linear regression can be used to uncover the relationships that
exist in construction (Table 1).

Elements of a regression equation (linear, first-order model)
Regression equation: Y¼a+bx+ξ
y is the value of the dependent variable (y), what is being predicted or
explained.
a is a constant, equals the value of y when the value x¼0.
b is the coefficient of x, the slope of the regression line, how much y changes
for each change in x.
ξ is the error term, the error in predicting the value of y, given the value of x.

Assumptions of linear regression
(1) Both the independent (x) and the dependent (y) variables are measured at
interval or ration level.
(2) The relationship between the independent (x) and the dependent (y)
variables is linear.
(3) Errors in the prediction of the value of y are distributed in a way that
approaches the normal curve.
(4) Errors in the prediction of the value of y are all independent to one another.
(5) The distribution of the errors in the prediction of the value of y is constant
regardless of the value of x.