Ch 14 (15 in book) Correlation & Regression
the more data points varying from a straight line, the closer the Pearson correlation value is to _____
0
a set of 10 pairs of scores has ΣX=20, ΣY=30, ΣXY=74, what is the value for SP
14
when to use r
A correlation coefficient is used when the research question asks about the association or relationship between two sets of scores.
when to use t
A t test is used when the research question asks about a possible difference between the means of two sets of scores.
regression equation for Y
Y^ (y hat) = bX + a
what is one thing r and the t test have in common?
they require that the scores be from the same participant or from linked participants.
deviation
x-Mx, y-My
r^2
coefficient of determination
t or f: A negative correlation indicates that decreases in one variable tend to be accompanied by decreases in the other variable.
f
t or f if data points are tightly clustered around as line that slopes from left to right, then a good estimate of the correlation would be +.90
f (-.90)
t or f- the value of SP can never be less than zero
false (sp can be -)
as sample size decreases, magnitude of correlation needed for significance _______es
increases (a large correlation is needed before you can be sure with a small sample)
a =
My- bMx
negative correlation
two variables go in opposite directions- inverse relationship
positive correlation
A correlation where as one variable increases, the other also increases, or as one decreases so does the other. Both variables move in the same direction.
a positive slope indicates
x and y increase (and move up and to the right)
in a negative slope,
y decreases when x increases
A set of n = 5 pairs of X and Y values has X = 10, Y = 20, and XY = 60. For this set of scores, the value of SP is ________.
20
r=
Pearson correlation
b=
SP/SSx
A negative value for a correlation indicates ________. a. decreases in X tend to be accompanied by decreases in Y b. decreases in X tend to be accompanied by increases in Y c. a much stronger relationship than if the correlation were positive d. a much weaker relationship than if the correlation were positive
b
Which of the following pairs of variables should produce a correlation near 0? a. model year (2003, 2004, etc.) and price for a used Honda b. driving distance from college and weekly cost of gas for a group of commuting college students c. number of hours studying and number of errors on a math exam d. IQ and weight for a group of third-grade students
d
As the sample size gets larger, the size of the correlation necessary for significance ____.
gets smaller
Pearson correlation
measures the degree and the direction of the linear relationship between two variables (degree to which x and y vary together/degree to which x and y vary separately)
coefficient of determination
measures the proportion of variability in one variable that can be determined from the relationship with the other variable
pearson df
n-2
A college professor reports that students who finish exams early tend to get better grades than students who hold on to exams until the last possible moment. The correlation between exam score and amount of time spent on the exam is an example of ____ correlation
negative
regression
statistical technique for finding the best-fitting straight line
SP
sum of products of deviations
t or f: Assuming that other factors are constant, a correlation of r = +0.68 will result in more accurate predictions than a correlation of r = −0.95.
t
t or f: It is possible for the regression equation to have none of the actual (observed) data points located on the regression line
t
For a hypothesis test for the Pearson correlation, the null hypothesis states that ________.
the population correlation is 0
The regression equation is determined by minimizing ____.
the total squared error between the predicted Y values and the actual Y values
