Correlation and Regression

Psychology 290

Correlation and Regression

1. The following numbers are the data showing grades on a midterm and the time (in hours) spent studying for the midterm.

Time Spent Studying (Hours) / Exam Grade
5 / 64
15 / 88
14 / 87
8 / 71
7 / 77
10 / 80
4 / 55
9 / 63
3 / 68
12 / 84

a)  If the researcher performs a two-tailed test, with an α = 0.05, does the correlation reach significance?

r:

tails:

df:

sig:

b)  Use a regression equation to predict the exam grades for the following study times:

1. 5 hours

Y=2.315 (5) + 53.56

=~65%

c)  Compare your answer in b to the Exam Grade for Participant 1. Explain any differences.

Close à64% - 65%

Not perfect due to error (not 100% correlation, so not 100% accurate)

**only compare last table in spss (when the 4 are created -> use the coefficients one)

SPSS CHEAT SHEET

CORRELATION & REGRESSION

CORRELATION:

Input all your data into separate columns. Then…

à ANALYZE

à CORRELATE

à BIVARIATE

à TOGGLE VARIABLES

à SELECT PEARSON R

à SELECT 1 OR 2 TAILED TEST (depending on hypothesis)

à CLICK OK

INTERPRETING THE OUTPUT:

Correlations

VAR00001 / VAR00002
VAR00001 / Pearson Correlation / 1 / -.938(**)
Sig. (2-tailed) / .001
N / 8 / 8
VAR00002 / Pearson Correlation / -.938(**) / 1
Sig. (2-tailed) / .001
N / 8 / 8

** Correlation is significant at the 0.01 level (2-tailed).

In each instance SPSS compares each variable to each other variable. Pearson correlation is the degree to which the variables co-vary. If the r value is positive the variables vary in the same direction. If the r value is negative, the variables vary in opposite directions. The significance of the correlation is indicated in the second row. If the significance is smaller than the a level it is significant.

REGRESSION:

Input all your data into separate columns. Then…

à ANALYZE

à REGRESSION

à LINEAR

à DETERMINE YOUR PREDICTOR AND CRITERION VARIABLES

à TOGGLE PREDICTOR VARIABLE INTO “INDEPENDENT” COLUMN

à TOGGLE CRITERION VARIABLE(S) INTO “DEPENDENT” COLUMN

à CLICK OK

INTERPRETING THE OUTPUT:

Coefficients(a)

Model / Unstandardized Coefficients / Standardized Coefficients / t / Sig.
B / Std. Error / Beta
1 / (Constant) / 61.064 / 1.508 / 40.485 / .000
VAR00003 / 1.855 / .153 / .974 / 12.110 / .000

a Dependent Variable: VAR00004

When you run a linear regression, SPSS outputs include a correlation output, ANOVA output and coefficients output. The coefficients output provides all the necessary details for constructing a regression equation (y = bx + a).

A = Column B for (Constant)

B = Column B for independent variable

E.G. Y’ = (1.855)X + 61.064