Exploring Statistical Methods
Multiple Linear Regression
HK 396 Quantitative Research Methods
The following questions pertain to the article:
Chu et al. (2010). The relationship between biomechanical variables and driving
performance during the golf swing. Journal of Sports Sciences, 28, 1251-1259.
1) Clearly state the purpose of the study.
Identify and validate the most important factors contributing to driving performance in a diverse
group of golfers.
2) Specifically describe the dependent variables and generally describe the
independent variables.
Dependent ball velocity
Independent (predictor variables)  tilts/ kinematic angles: trunk, arm, legs,
kinetic: ground reaction force
-measured at: Top, Acceleration, Last 40 ms, & Impact
3) What type of linear regression was used in addressing the purpose? Discuss
some pros and cons of this method compared to a hierarchical regression.
stepwise linear multiple regression  Stepwise regression is a statistical method to determine
whether certain independent variables are linearly related to a dependent variable. It adds
independent variables into a linear model sequentially based on the variables’ significance. With
every variable added into the model, all variables already in the model are reviewed and may be
removed if no longer significant.
- It may wrongly interpret the significance of that variable because the combination of
some variables is what might produce different results  just does mathematical
perspective and is very dependent on data set (removed variable after significance >
.1 was attained)
- Hierarchal  has bias as to what is most significant, the researchers have hypothesis
so there is a plan
- Pros: gives you best predictors of data set
- Cons: heavily dependent on data set
4) What was the purpose of performing an a prior power analysis?
Power  ability to detect difference when one really exists
To determine the adequate number of participants in order to achieve
statistical power (Beta).
*The more predictor variables you have
Dr. Sasho MacKenzie – HK 396
5) Why was it important to include participants with a wide range of golfing
ability and hence ball speed? Why not use a large group of professionals
with a smaller standard deviation of ball speeds?
Professional golfers all have good form due to vast amount of time spent
golfing, all similar swings. Using large array of golfing abilities allows the
researchers to distinguish what factor the amateurs are doing right in
comparison to pros.
- Technical  based on how regression works: want a variability
in the variables (ie. Wrist angle)  want a range in dependent
and independent variables
6) Describe the difference between a beta coefficient and standardized beta
coefficient? I.e., what information does each statistic provide?
- beta coefficient is the change of dependent variable in unit of standard deviation when an independent variable is
changed for one standard deviation.
- standardized beta coefficient  the conversion factors that allow you to
formulate an equation to make predictions about the dependent variable
* The larger the size of the variable that is entered the smaller it
becomes as a coefficient
**The standardized coefficient is more important than the unstandardized
coefficient because it tells you its significance
7) Four models, distinguished by the time during the downswing the
independent variables were measured, were analyzed. Which model
demonstrated the best ability to predict ball speed after impact? For that
model, what independent variable was the strongest predictor of ball speed?
- The 3rd because it the highest R^2  Predicted 75% variability
in ball speed
8) For all participants, ball speed was 61 ± 8.7 m/s. Considering Model 3 (Table
III) and referring to Table II, if a golfer’s wrist hinge angle increased by 13° at
40 ms before impact, how much would their associated ball speed change
by?
- One change of 13 degrees is equivalent to one standard
deviations so ball speed should go up by 3.04 m/s (0.349*8.7).
Dr. Sasho MacKenzie – HK 396