The Application of Linear Regression to Range-of-Fire Estimates Based on the Spread of Shotgun Pellet Patterns

Abstract

Abstract A series of shotgun pellet patterns were fired at ranges that varied from 3.9 to 15.2 m (10 to 50 ft) using a 12-gauge cylinder-bored shotgun firing No. 2 chilled shot cartridges. The spreads of the pellet patterns were measured in two ways: the radius of the smallest circle that would enclose the entire pattern was measured with a transparent overlay and the square root of the area of the smallest rectangle that would enclose the pattern was calculated. Linear regression analysis was applied to sets of data for shots at three, five, and nine ranges. For both measures of pattern spread the linear regression gave correlation coefficients greater than 0.99, indicating that a linear relationship existed between the measures of the pattern spreads and the range of fire. The confidence intervals for range-of-fire estimates at the 95% confidence level were calculated for each set of data. As expected, increasing the number of test-fired patterns decreases the confidence interval and so improves the range-of-fire estimates obtained from the test-fired patterns.