SW318 Social Work Statistics Slide 1

1
The data
We are interested in the relationship between
family size and number of credit cards.
2
The scatter diagram or scatterplot
The dependent variable is plotted on the Y or
vertical axis.
The independent variable is plotted on the x or
horizontal axis.
3
The mean as the best guess
Without taking into account the independent
variable, our best guess for the number of credit
cards for any subject is the mean, 7.0.
4
Errors using the mean as estimate
Errors are measured by computing the difference
between the mean and each Y value, squaring the
differences, and then summing them. When we
compute the answer in SPSS, it will tell us that
the total amount of error is 22.0.
5
Possible other lines that reduce error
There are numerous other lines that we could draw
that more closely fit the pattern of the data
points.
6
The regression line
The best line is the regression line which
minimizes the error (the best fitting or least
squares line)
7
The equation for the regression line
SPSS will give us the formula for the regression
line in the form Y a bX, or for these
variables Number of Credit Cards 2.871 .971
x Family Size
8
PRE reduction in error
SPSS also tells us the amount of error using only
the mean and using the regression line.
Error using mean 22.000
Error using regression line 5.486
Reduction in error 16.514
PRE measure 22.0-16.514 .751 22.0
9
PRE reduction in error
Error using mean 22.000
Error using regression line 5.486
Reduction in error 16.514
PRE measure 22.0-16.514 .751 22.0
10
Pearsons r correlation coefficient
The square root of r2 is Pearsons r, the
correlation coefficient.