4.11 Hazards in the use of Regression
Regression analysis is widely used and unfortunately if frequently misused.
There are several common abuses on linear regression that should be mentioned
- 1.
- Linear regression model may not be valid for extra plotion outside a certain range.
- 2.
- Influential points
\(A\) and \(B\) are known as influential points
- 3.
- Outlies or “bad” values (points)
- 4.
- Just because a regression analysis has indicated a strong relationship between \(Y\) and \(X\) doesn’t
imply that the variables are related in any casual sense. \begin {align*} Y & = \quad \text {number of certified mental patients per 10,000 estimated populations}\\ X_1 & = \quad \text {number of radio station lincenses issued in UK}\\ X_2 & = \quad \text {first name of president of the U.S.A} \end {align*}
\((1924-1937) \) Kendall and Yule
\begin {align*} \widehat {Y} & = 4.582+2.204X_1, \quad R^2=0.9842\\ H_0: \beta _1 & =0,\quad t_{cal}=27.312 \end {align*}
\begin {align*} \widehat {Y} & = -26.442+5.900X_2,\quad R^2=0.8709\\ H_0: \beta _2 &=0,\quad t_{cal}=8.996\\ \end {align*}
Both equations give nonsense relationship.
- 5.
- In some applications of regression the values of the independent variable required for the
predication of \(Y\) is unknown.
Example 4.11.1. Consider predicting maximum daily load on an electric power generation system from regression model relating the load to maximum daily temperature.
Questions on this section
Stuck on something here? Ask below and it stays attached to this topic.