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Ch. 1 Introduction to Simple Linear Regression
Terms in this set (15)
What is the relationship between the variables in simple linear regression?
The criterion variable (Y) is used to predict the value of the predictor variable (X).
What happens to simple linear regression when both the independent and dependent variables are scale (form a perfect straight line)? Why is this not likely in behavioral and social research?
Finding a linear equation that fits the given data would be easy and straightforward. B/c it is rare that the data perfectly linearly related
Pearson correlation coefficient/ correlation coefficient
a descriptive statistic that describes the linear relationship between two attributes. (r=...)
How do we choose the "best-fitting line"?
Take the line that (on average) comes closest to all of the scatter plot points
What is the line of best fit called?
(least squares) regression line** or
(least squares) prediction line
What is it called when there is only one predictor variable?
What is y hat? (Ŷ)
The predicted value of y
Error of prediction for a point
The value of the point minus the predicted value (the value on the line). (Y-Y')
Regression line equation
(Y' is the predicted score, b is the slope of the line, and A is the Y intercept)
MX, MY, sX, sY, and r
Mx= mean of x
MY= mean of y
sX=standard deviation of X
sY= standard deviation of Y
r= correlation between X and Y
How do you calculate slope b? (regression coefficient)
b = r sY/sX
(slope b= r times slope of x divided by slope of y)
How do you calculate intercept A?
A = MY - bMX
(intercept A= mean of Y minus slope b times mean of X)
What is the regression equation used for?
To find the predicted Y for a given value of X
The values of b and a can be used to explain the relationship between ___ & __.
X & Y
What is the equation for standardized regression?
ZY' = (r)(ZX)
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