Which statement about a regression line is true regarding the influence of outliers?

Which statement about a regression line is true regarding the influence of outliers?

• A. Outliers always increase the slope of the regression line
• B. Outliers can significantly affect both the slope and intercept
• C. Outliers have no effect on the regression line
• D. Outliers can only affect the intercept

Answer: (B)

The statement that outliers can significantly affect both the slope and intercept of a regression line is accurate. In regression analysis, an outlier is a data point that differs significantly from other observations. When such points are present, they can exert a disproportionate influence on the calculated slope and intercept of the regression line. If an outlier is far from the rest of the data in the predictor variable (x-axis), it can skew the slope, which is the measure of how much the response variable (y-axis) changes for a unit change in the predictor. Additionally, if the outlier lies well above or below the general trend of the other data points, it can impact the intercept, which is where the regression line crosses the y-axis. Thus, outliers play a crucial role in determining the overall fit of the regression model by affecting both components necessary to define the line's equation. The influence of outliers is a fundamental concept in regression analysis, and understanding this impact is essential for ensuring accurate modeling and interpretation of relationships in statistical data.

The statement that outliers can significantly affect both the slope and intercept of a regression line is accurate. In regression analysis, an outlier is a data point that differs significantly from other observations. When such points are present, they can exert a disproportionate influence on the calculated slope and intercept of the regression line.

If an outlier is far from the rest of the data in the predictor variable (x-axis), it can skew the slope, which is the measure of how much the response variable (y-axis) changes for a unit change in the predictor. Additionally, if the outlier lies well above or below the general trend of the other data points, it can impact the intercept, which is where the regression line crosses the y-axis. Thus, outliers play a crucial role in determining the overall fit of the regression model by affecting both components necessary to define the line's equation.

The influence of outliers is a fundamental concept in regression analysis, and understanding this impact is essential for ensuring accurate modeling and interpretation of relationships in statistical data.