Respuesta :
In the regression line y = a+ bx+ e, a is the slope of the regression line.
The above statement is False.
The correct Statement is :
The linear regression line has an equation of the form Y =a + bX
where, Y is called the dependent variable or response.
X means independent or predictor or explanatory variable.
a is the y-intercept and b is the slope of the line.
Regression Line:
A regression line is a statistical tool that shows the correlation between two variables. Specifically, it is used when the variation of one (the dependent variable) depends on changes in the value of the other (the independent variable).
Simple linear regression has two cases:
- The equation is Y on X, and the value of Y changes as the value of X changes.
- The formula is X over Y, and the change in X varies with the deviation of the Y variable.
The formula for the least squares regression line (LSRL) from Y to X is:
Y=a + bX + ɛ
where,
Y is the dependent variable.
a is the Y intersection.
b is the slope of the regression line.
X is the independent variable.
ɛ is the residual (error).
and
b = (N∑XY-(∑X)(∑Y) / (N∑X2– (∑X)2) ;
and
a = (∑Y – b ∑X) / N
where, N is the total number of observations.
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