Answer to Question #209963 in Statistics and Probability for Eli

Question

1. Why it is dangerous to make predictions beyond the scope of what you have observed in your data set

2. give at least two examples of situations where in predictions of the value of the dependent variable using the equation of the regression line would be meaningless

Answer 1

1.Why it is dangerous to make predictions beyond the scope of what you have observed in your data set

This is because the more the predictions are made outside the scope of data, the more the chances of the model of the data set to fail due to disparities between the assumptions and the true values.

2.Give at least two examples of situations where in predictions of the value of the dependent variable using the equation of the regression line would be meaningless

(I). The situation where the repeated responses of $y$ are not independent of each other. In an ideal case, the dependent variable is denoted $y$ and the independent variable is denoted $x$. The equation for a linear regression line is $y=a+bx$ with $x$ as the independent variable and $y$ as the dependent variable. The intercept (the value of $y$ when $x$ = 0) is $a$, while the slope of the line is $b$.

(II). The situation where the standard deviation of $y(\sigma)$ is different for all values of $x$. In this case the value of standard deviation will be determined easily hence the prediction of the value of the dependent variable by regression equation will be of no significance.