Regression
analysis is a statistical tool for the investigation of relationships between
variables. . In regression analysis data used to describe relationship between
variables that are measured on interval scale. Regression allows you to predict
variables based on another variable. In statistical modeling, regression analysis is a statistical process for
estimating the relationships among variables. It includes many techniques for
modeling and analyzing several variables, when the focus is on the relationship
between a dependent variable and one or more independent variables (or
'predictors').Usually, the investigator seeks to ascertain the causal
effect of one variable upon another the effect as price increase upon demand, The
relationship between the two variables is estimated as a linear or straight
line relationship, defined by the equation: Y = aX + b where b is the intercept
or the constant and a, the slope. The line is mathematically calculated such
that the sum of distances from each observation to the line is minimized. By
definition, the slope indicates the change in Y as a result of a unit change in
X. The straight line is also called the regression line or the fit line and a
is referred to as the regression coefficient. The method of calculating the
regression coefficient (the slope) is called ordinary least squares, or OLS.
OLS estimates the slope by minimizing the sum of squared differences between
each predicted (aX + b) and the actual value of Y. One reason for squaring
these distances is to ensure that all distances are positive. A positive
regression coefficient indicates a positive relationship between the variables;
the fit line will be upward sloping). A negative regression coefficient
indicates a negative relationship between the variables; the fit line will be
downward sloping. The test of significance of the regression slope is a key
test of hypothesis regression analysis that tells us whether the slope a is
statistically different from 0. To determine whether the slope equals zero, a
t-test is performed. As a general rule when observations on the scatter plot
lie closely around the fit line, the regression line is more likely to be
statistically significant in other words; it will be more likely that the two
variables are – positively or negatively – related. Fortunately, SPSS
calculates the slope the intercept standard error of the slope, and the level
at which the slope is statically significant. The investigator also typically
assesses the “statistical significance” of the estimated relationships, that
is, the degree of confidence that the true relationship is close to the
estimated relationship. Regression techniques have long been central to the
field of economic statistics. Increasingly, they have become important to
lawyers and legal policy makers as well.

Regression
and correlation are actually fundamentally the same statistical procedure. The
difference is essentially in what your purpose is - what you're trying to find
out. In correlation we are generally looking at the strength of a relationship
between two variables, X and Y, where in regression we are specifically
concerned with how well we can predict Y from X. Examples of the use of
regression in education research include defining and identifying under
achievement or specific learning difficulties, for example by determining
whether a pupil's reading attainment (Y) is at the level that would be
predicted from an IQ test (X). Another example would be screening tests,
perhaps to identify children 'at risk' of later educational failure so that
they may receive additional support or be involved in 'early intervention'
schemes. The chief advantage of regression analysis is that variables
relationship is based on mathematical equation. This in turn allows more
accurate prediction of one variable from knowledge of other variable which is
the objective of regression analysis.

Regression
analysis is used when two or more variables are thought to be systematically
connected by a linear relationship. In simple regression, we have only two –
let us designate them x and y and we suppose that they are related by an
expression of the form y = b0 + b1 x + e. We’ll leave aside for a moment the
nature of the variable e and focus on the x - y relationship. y = b0 + b1 x is
the equation of a straight line; b0 is the intercept (or constant) and b1 is
the x coefficient, which represents the slope of the straight line the equation
describes. To be concrete, suppose we are talking about the relation between
air temperature and the drying time of paint. We know from experience that as x
(temperature) increases, y (drying time) decreases, and we might suppose that
the relationship is linear. By measuring with a ruler, we could then determine
the slope and intercept of this line.

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