# EXAM REVIEW REGRESSION AND CORRELATION.doc

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University of Toronto Scarborough

Psychology

PSYB07H3

Douglas Bors

Fall

Description

30
STRAIT STTC MARK
30 STRAIT STTC MARKAFTER MIDTERM EXAM NOTES
REGRESSION AND CORRELATION
Relation between Two Variables
Regression and Correlation: In both cases, y is a random variable
beyond the control of the experimenter. In the case of correlation, x is
also a random variable. In the case of regression, x is treated as a fixed
variable. (As if there is no sampling error in x.)
Regression: you are wishing to predict the value y on the basis of the
value of x
-how change are we to expect with a change in 1 variable to put into
units of measurement
-i.e. predicting final mark based on midterm mark
Correlation: you are wishing to express the degree of the relation
between x and y
-like the phi coefficient degree of relation between the two variables
-how good/how much error in the prediction?
-if x and y are unrelated, the best predictor of y is the mean of y
-you have to look for something that minimizes the error
Scatter Plot
-X axis (abscissa) = predictor variable
-Y axis (ordinate) = criterion variable
Example: GPA vs. statistic mark:
Positive Negative Perfect None
-linear relationship always but there are non relationship forms of
regression and correlation
-the denomination of positive, negative etc, has nothing to do with the
quality of the relation
-Positive: (+) changes in one variable leads to (+) change in second
variable-Negative: (+) changes in one variable leads to (-) changes in second
variable (?)
-Perfect: change in produces predicted changes in y
Covariance
-is a number reflecting the degree to which two variables vary or change
in value together
(x − x) y −(y)
C x =yO V
n −1
n= the number of xy pairs
Example: collecting reaction time and error scores
-If a subject is slow (high x) and accurate (low y), then the d score for
the x will be
positive and the d score for the y will be negative; their product will be
negative.
-If a subject is slow (high x) and inaccurate (high y), then the d score for
the x will be
positive and the d score for the y will be positive; their product will be
positive.
-If a subject is fast (low x) and accurate (low y), then the d score for the
x will be
negative and the d score for the y will be negative; their product will be
positive.
-If a subject is fast (low x) and inaccurate (high y), then the d score for
the x will be
negative and the d score for the y will be positive; their product will be
negative.
**d score = deviation score (score minus mean)Scatter plots of the data:
There is a trend after all
-There is no linear relationship between x and y but a perfect
relationship
-always look/draw scatterplot to make conclusions on trends • Scale issues
Example: i.e. using minutes vs. seconds
(Sec.) (Min.)
-the absolute value of the covariance is a function of the variance of x
and the variance of y thus, a covariance could reflect a strong relation
when the two variance are small, but maybe express a weak relation
when the variance are large
For a perfect relationship:
-linear relation is one in which the relation can be most accurately
represented by straight line
-linear transformation is represented by:
x = c (x ) + c
n e 1 w o l d2
-general equation for a straight line: y = bx + a a is the y intercept
and b is the slope
Δy

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