Master Dependent and Independent variables in Regression for CBSE Class 11 Applied Mathematics. Learn with solved examples, MCQs, and practice problems.
The independent variable, often denoted by x, is the predictor variable that is manipulated or controlled to observe its effect on another variable. In regression analysis, it serves as the input that explains the variation in the dependent variable. For example, in studying the relationship between study hours and exam scores, study hours act as the independent variable.
Step 1: Identify the variable that influences the outcome. In a study of fuel consumption (y) based on distance traveled (x), distance is the cause.
Step 2: Assign x to distance.
Answer: x = distance traveled.
The dependent variable, denoted by y, is the outcome variable whose value depends on the changes in the independent variable. It is the variable being predicted or explained by the regression model. In the linear regression equation y = a + bx, y represents the dependent variable.
Step 1: Identify the variable being measured as the result. In a study of salary (y) based on years of experience (x), salary is the outcome.
Step 2: Assign y to salary.
Answer: y = salary.
Regression analysis quantifies the relationship between the independent variable x and the dependent variable y. The slope coefficient b indicates the change in y for every unit change in x. This mathematical dependency allows for forecasting future values based on observed data.
Step 1: Given y = 10 + 2x and x = 5.
Step 2: Substitute x = 5 into the equation: y = 10 + 2(5).
Step 3: Calculate: y = 10 + 10 = 20.
Answer: y = 20.