A simple linear regression equation is to be constructed to determine if there is a linear relationship between a response variable(Y)and an explanatory variable(X). A random sample of size n has been collected and the values x_iand y_ifori = 1, 2, ..., nhave been recorded. The residuals(e_i)in this analysis are defined as the difference between the observed values of Y and the values of Y predicted by the regression equation.

The scatterplot or residual plots can be used to see if the regression equation is an appropriate model for the data. An assumption required for the simple linear regression equation to be valid is:

a) the residuals are constant

b) X and Y are independent

c) the variance of X is equal to the variance of Y

d) the relationship between X and Y is linear