Question

A regression equation was fit to the data showing the number of hours of training time received by production line workers and the time it took (in minutes) for them to trouble shoot their last process problem and the following histogram of residuals obtained. Based on this histogram of the residuals, we can say that the Histogr am (resporse is Trouble Shooting) 1 0 -1 0 1 2 3 Residual A. nearly normal condition is satisfied B. equal spread condition is satisfied. C. linearity condition is not satisfied. D. independence condition is not satisfied. Fre que ncy t

Answer 1

The goal of regression is to explain the variation in the dependent variable using the independent variable. For this, as much of variation that can be explained must be covered under the explained variation.
The unexplained variation is the residuals. Hence we need to check that there is no underlying pattern in the residuals indicating that there could be more variables that could explain the variation in the dependent variables.

Hence we check for any pattern in the residuals and also check that the residuals are normally distributed so that they sum up to zero.

The histogram helps us to understand that the residuals are normally distributed as per the assumptions of linear regression.

Correct option: A. nearly normal condition is satisfied.