Chapter 4 Flashcards
Correlation and Prediction
Correlation coefficient
linear relationship
Y=ax+b
the statistically examined relationship between variables
Correlation
helps describe reaction and in some cases predict outcomes
Relationship
the statistical association between variables
Persons product-moment correlation coefficient (PPM)
symbolized my r
measurement of the relationships between two variables
Correlation coeficient
can be either positive or negative
magnitude between -1 and 1
Positive r
indicates that participant scored above the mean on one variable X, and will be above the mean on the second variable Y
Negative r
the scores above the mean on X will be generally be below the mean on Y
Direct relationship
positive relationship
Ex: low values for chin-ups and low values for pull-ups
Indirect relationship
negative or inverse relationship
Ex: examine body weight vs. pull-ups, and you can see that high body weights are generally paired with low pull-up scores.
Scatterplot
graphic representation of the correlation between two variables
Zero correlation
scatterplot would demonstrate nothing even resembling the straight line
Coefficient of determination = r^2
or the personage of shared variance
- square of the correlation coefficient
- this value represent the proportion of shared variance between the two measures in question
Ex: if r = 0.9 the r^2 would be 0.81 which mean the percentage of shared variance 81%
Non-predicted variance
unexpected performance or the rest of percentage from shared variance
100-81=19%
Negative correlation
Reasons:
1) result from two measures having opposite scoring scales
Ex: the distance covered in in a 12-minute run or the time required to run 1.5 miles
2) two measures have a true negative relationship
Ex: measuring the body weight and pull-ups
Limitation of r
1) if between two variables happened to have a curvilinear relationship
2) if the correlation is not an indication of a cause-and-effect relationship
3) effect of variance or range of of the data on the magnitude of r
THE REASON OF GRAPHING THE RELATIONSHIPS USING THE SCATTERPLOT TECHNIQUE
Curvilinear relationship
no linear relationship between variables
Prediction
a valuable use of correlation
Regression
simple linear prediction or a statistical method used to predict the criterion, outcome
Y - dependable variable
true
X - in-dependable variable
true
Formula for prediction
Y = bX + c
Errors in prediction (E)
E = actual Y value - predicted Y value
represents the inaccuracy of our predictions of Y based on the prediction equation
If the errors can be minimized, prediction can be improved
true
Standard error of estimate (SEE)
or standard error of prediction
statistic that reflects the average amount of error in the process of prediction Y from X
