Statistical Methods for Psychology

Exercises 285

Exercises

9.1 The State of Vermont is divided into 10 Health Planning Districts, which correspond roughly

to counties. The following data for 1980 represent the percentage of births of babies under

2500 grams (Y), the fertility rate for females younger than 18 or older than 34 years of age

( ), and the percentage of births to unmarried mothers ( ) for each district.^17

District YX 1 X 2

1 6.1 43.0 9.2

2 7.1 55.3 12.0

3 7.4 48.5 10.4

4 6.3 38.8 9.8

5 6.5 46.2 9.8

6 5.7 39.9 7.7

7 6.6 43.1 10.9

8 8.1 48.5 9.5

9 6.3 40.0 11.6

10 6.9 56.7 11.6

a. Make a scatter diagram of Yand.

b. Draw on your scatter diagram (by eye) the line that appears to best fit the data.

9.2 Calculate the correlation between Yand in Exercise 9.1.

9.3 Calculate the correlation between Yand in Exercise 9.1.

9.4 Use a t test to test : r50 for the answers to Exercises 9.2 and 9.3.

9.5 Draw scatter diagrams for the following sets of data. Note that the same values of Xand Y

are involved in each set.

123

XY XY XY

22 24 28

34 32 36

56 58 54

68 66 62

9.6 Calculate the covariance for each set in Exercise 9.5.

9.7 Calculate the correlation for each data set in Exercise 9.5. How can the values of Yin

Exercise 9.5 be rearranged to produce the smallest possible positive correlation?

H 0

X 2

X 1

X 1

X 1 X 2

Splines (9.6)

Loess (9.6)

Sum of squares of Y( ) (9.7)

Standard error of estimate (9.7)

Residual variance (9.7)

Error variance (9.7)

Conditional distribution (9.7)

Proportional reduction in error

(PRE) (9.7)

Proportional improvement in prediction

(PIP) (9.7)

Array (9.8)

Homogeneity of variance in arrays (9.8)

Normality in arrays (9.8)

Conditional array (9.8)

Conditional distributions (9.8)

Marginal distribution (9.8)

Linearity of regression (9.13)

Curvilinear (9.13)

Range restrictions (9.14)

Heterogeneous subsamples (9.14)

SSY

(^17) Both X 1 and X 2 are known to be risk factors for low birthweight.