How much output variable will change?

In a simple linear regression model (One independent variable), If we change the input variable by 1 unit.

How much output variable will change?
A . by 1
B . no change
C . by intercept
D . by its slope

View Answer

Answer: D

Explanation:

What is linear regression?

Linear regression analysis is used to predict the value of a variable based on the value of another variable. The variable you want to predict is called the dependent variable. The variable you are using to predict the other variable’s value is called the independent variable.

Linear regression attempts to model the relationship between two variables by fitting a linear equation to observed data. One variable is considered to be an explanatory variable, and the other is considered to be a dependent variable. For example, a modeler might want to relate the weights of individuals to their heights using a linear regression model.

A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable. The slope of the line is b, and a is the intercept (the value of y when x = 0).

For linear regression Y=a+bx+error.

If neglect error then Y=a+bx. If x increases by 1, then Y = a+b(x+1) which implies Y=a+bx+b. So Y

increases by its slope.

For linear regression Y=a+bx+error. If neglect error then Y=a+bx. If x increases by 1, then Y = a+b(x+1) which implies Y=a+bx+b. So Y increases by its slope.