The regression between height and age follows y=a+bx. The curve is -
Ans. is 'c' i.e., Straight line Regression o Regression is not the same as correlation, but the two are related. Correlation quantifies how well the two variables X and Y are related together, but one can not predict one unit change of one variable will cause how much change of the other variable . For this regression equation is needed. o If two variables are highly correlated, it then becomes possible to predict the value of the dependent variable from the value of the independent variable by using regression teachnique .Regression analysis is the mathematical modelling to describe the effect that one or more independent variables have on a dependent variable. o So, when there is distinct relation between two variables, one has to perform both the calculations, i.e. correlation coefficient followed by regression. If no relationship is established in correlation coefficient, regression is not required at all. Types of Regression There are following types of regression :? 1. Linear Regression In Linear Regression the influence of independent (explanatory) variable on a dependent (response) variable is linear, i.e. change in the independent variable will cause a change in the dependent variable that can be depicted by a straight line. Linear regression may be of two types: i) Simple linear regression: - Expresses the effect of one independent (X) variable on dependent variable (Y)- y = a + bx where ? a = is a constant Ida intercept constant b is the regression coefficient x is the independent variable. y = is the dependent variable whose value is to be found out. ii) Multiple linear regression:- Expresses the effect of more than one independent variables on a dependent variable. 2. Curvilinear regression In some situations, the influence of independent variable on the dependent variable is like a curve (instead of straight line). The suffix 'linear' is still there because the curve can be conveed to line after some mathematical transformation such as logarithm and square. Curvilinear regression, similar to linear regression, may be of two types: i) Simple curvilinear regression:- influence of one independent variable on a dependent variable, with some power on independent variable y = a + b(x)6 ii) Multiple Curvilinear regression: Influence of more than one independent variables on a dependent variable, with some power on independent variables. y = a + b (x,)2 + C(X2)3 + d(x3)3 3. Non-linear regression Third type of regression is called non-linear regression which has curve like relationship. However; this term is used only for the relationship that cannot be conveed to linear form by any transformation. Coming to the Question o In the regression equation there is no square or logarithm. That means it is linear regression. o There is only one independent variable (x). o Therefore, this is simple linear regression which can be depicted by a straight line.
Hyperbola
Sigmoid
Straight line
Parabola