Researchers at Victoria University wanted to determine the factors that affect precision in shooting air pistols. "Inter- and Intra-Individual Analysis in Elite Sport: Pistol Shooting," Journal of Applied Biomechanics, 28-38, 2003. The explanatory variables were
x1: Percent of the time the shooter's aim was on target (a measure of accuracy)
x2: Percent of the time the shooter's aim was within a certain region (a measure of consistency or steadiness)
x3: Distance (mm) the barrel of the pistol moves horizontally while aiming
x4: Distance (mm) the barrel of the pistol moves vertically while aiming
(a) One response variable in the study was the score that the individual received on the shot, with a higher score indicating a better shooter. The regression model presented was y̅ = 10.6 + 0.02x1 - 0.03x3. The reported P-value of the regression model was 0.05. Would you reject the null hypothesis H0: b1 = b3 = 0?
(b) Interpret the slope coefficients of the model in part (a).
(c) Predict the score of an individual whose aim was on target x1 = 20% of the time with a distance the pistol barrel moves horizontally of x3 = 12 mm using the model from part (a).
(d) A second response variable in the study was the vertical distance that the bullet hole was from the target. The regression model for this response variable was y̅ = -24.6 -0.13x1 + 0.21x2 + 0.13x3 + 0.22x4. The reported P-value of the regression model was 0.04. Would you reject the null hypothesis H0: β1 = β2 = β3 = β4 = 0?
(e) Interpret the slope coefficients of the model in part (d).