Fundamentals
The y-intercept is the value of Y when X equals:
0
The regression line, or best-fitting straight line to a set of data points, is the line associated with the
smallest possible value of __________________.
Sum of Squares
What does “n” represent?
Sample size
A positive correlation means that as the values of one factor increase, the values of the second factor ____.
A negative correlation means that as the values of one factor increase, the values of the second factor ___.
increase.
decrease
What symbol represents correlation?
(r)
Linear regression is used to predict values of Y (the ____ variable), given values of X (the ___ variable).
criterion
predictor
The regression line is the line that makes the value of SS the:
smallest
What does p < .05 mean?
Statistically significant
A correlation is a statistical procedure used to describe the ____ and ___ of the linear relationship between two factors.
strength
direction
What happens to the value of r the closer that data points fall to the regression line?
The correlation coefficient increases closer
to r = ±1.0.
Equasion of slope
SSxy/SSx
AKA ---- SP/SSx
Why does Y — have a hat? (ŷ)
Ŷ is the predicted value of Y, given values of X.
If p = .20, what is the conclusion?
(Not significant)
The correlation coefficient symbol:
(r)
An instructor reports that as the number of student interruptions during class decreases, student scores on in-class quizzes increase.
Is this an example of a positive correlation or a negative correlation?
Negitive (one going up, one going down)
Regression line formula:
Y = bX + a.
SSXY, which is the sum of products (SP), determines whether the slope of a straight line is:
positive or negative.
If R² = .25, how much variance is explained?
(25%)
Which of the following indicates the strongest correlation?
1. r = −.57
2. r = +.78
3. r = −.90
4. r = +.88
-.90
The correlation coefficient measures the:
variance
AKA
distance that data points fall from the regression line.
Formula for 'a' from regression line:
MY − (b)MX.
(Mean of Y values) - (slope)(Mean of X values)
F(1, 6) = 28.83, p < .05, R^2 =.83, using the following equation: Ŷ = −0.57X + 5.74.
What is 1? What is 6?
What is 28.83?
What does p<.05 imply?
1 → df for regression (numerator)
6 → df for error/residual (denominator)
28.83 → F → test statistic
p < .05 → Means the model is statistically significant
The degrees of freedom for regression variation, or degrees of freedom numerator, are equal to:
The degrees of freedom for residual variation, or degrees of freedom denominator, are equal to the sample size minus: __.
the number of predictor variables.
2
Given points (1,3), (2,2), (3,1), what is the slope?
What is a?
500 points for each.
b = [−1] --> Slope
(2/-2)
a = [4] --> y-intercept
(-2)-(-1)(2)
Mx --> 2 My --> 2
(x-Mx)
1-2 = -1 --
2-2 = 0 --
3-2 = 1 --
(y-My)
3-2 = 1
2-2 = 0
1-2 = -1
(X−Xˉ)2
1
0
1
(Y−Yˉ)2
1
0
1
(X−Xˉ)(Y−Xˉ)
-1
0
-1
SSX=∑(X−Xˉ)2=
1+0+1
=2
SSXY=∑(X−Xˉ)(Y−Yˉ)
=−1+0+(−1)
=−2
2/-2 =
(-1) = slope
If Y = 2 + 3X, what is Y when X = 4?
14