Correlation Examples Flashcards
Simple Linear Regression Rationale
Oftentimes, it is not only desired to determine how the scores of one distribution are related to the scores of another distribution, but to take advantage of this relationship to use for predicting one score given the other.
Simple Linear Regression Purpose
for prediction
Regression
a statistical technique which considers using the
relationship between two or more variables for
prediction
Linear Regression
a regression technique wherein the regression function is taken to be of the linear form (i.e., the use of a linear
equation for prediction)
Simple Linear Regression
a linear regression which only uses one predictor (x) to explain/predict a response (y)
Simple Linear Regression Formula
y = B0 + B1x + e
y
Response value
B0
- y-intercept (of the regression line)
- when the scope of the model includes X = 0, B0 gives the mean of the probability distribution of Y at X = 0. When the scope of the model does not cover X = 0, B0 does not have any particular meaning as a separate term in the regression model
B1
- slope parameters
- the slope of the regression line
- it indicates the change in the mean of the probability distribution of Y per unit increase in X
x
the value of the predictor variable
e
the random error component
Residual (ith) [Prediction Error]
the difference between the observed value Yi and the corresponding fitted value ^Yi, denoted by ei (e.g. ei = Yi - ^Yi)
“i” in ei > 0 is what?
response i is UNDERESTIMATED
“i” in ei < 0 is what?
response i is OVERESTIMATED
“i” in ei = 0 is what?
response i is EXACT
