Question

What is the relationship between the algebraic equation for a straight line and the linear regression equation?

Answer 1

The equation of a straight line also called a linear equation is a one of the fundamental mathematical equation, which occurs in all areas of science when we need to calculate gradients of tangents, fit straight lines to data in statistics (linear regression). Actually an equation is a mathematical model, a statement of a perceived relationship between the variables. The advantage of mathematical models is the ability they provide to extrapolate and interpolate measured data. One of the easiest ways to develop a mathematical model involves graphing experimental data. In Mathematics a nonlinear problems are often reduced to linear problems which can be analysed more easily. In all these areas, and many more, one variable is related to another variable by multiplying it by a constant – just a number which does not
change – and adding another different, constant. Let there are two variables x and y and two constants are m and c. Thenequation of straight line is given by y=mx + c ; where m is the slope of the straight line and c is the y intercept is
The graph of any equation which fits this pattern is a straight line.

Basically a linear regression is the modeling of a conditional relationship between two variables as a straight line of best fit. In the relationship, y is conditional on x i.e. x is independent variable and y is the dependent variable .so the regression can be used to model the behavior of y given x outside of the known data set, such as in forecasting or we can say the technique of finding the line that best fits the pattern of the linear relationship (or in other words, the line that best describes how the response variable linearly depends on the explanatory variable).

Physical models of data are often used in engineering. e.g. models of the space shuttle were flown many times in wind tunnels before the shuttle's design was finalized and the shuttle was constructed. Molecular models help students and chemists understand the interaction between molecules and are often used to design therapeutic drugs.Behind each of these models is a set of measured numbers from which the model is developed and from which predictions of the model's behavior are made.

For example we show the relationship between high school GPA(independent variable) and university GPA(dependent variable )like:

Where straight line shows the shows the relationship between these variable called line of best fit.