Basic Statistics

REFERENCES 187

(c) Take the logarithm of X = GDP and repeat the steps in (a) and (b) using

(d) Explain why there is an increase in T when the logarithm of X is taken.

per capita as the X variable from the data given in Problem 12.4.

(a) Fit a least-squares regression line and compute T.

(b) Try a transformation on X and recompute T. Did it increase, and if so, why?

12.7 In Problem 12.4, a regression line was fitted using X = life expectancy and

Y = crude birth rate. The x = 68.7years and 7 = 21.4 births per 1000

population. Here, the effect of the three types of outliers will be explored.

(a) Add an outlier in Y that has a value (X, Y) of (68.7,44) and recompute the

(b) Remove the outlier added in (a) and add an outlier in X of (85,ll). Recom-

(c) Remove the outlier in (b) and add an outlier in X and Y (influential point)

(d) Compare the effects of these three outliers on the slope coefficient and the

log(GDP) as the X variable.

12.6 Plot the scatter diagram using the crude birth rate as the Y variable and GDP

regression line.

pute the regression line.

of (85,44). Recompute the regression line.

correlation coefficient.

REFERENCES

Afifi, A. A,, Clark, V. A. and May, S. [2004]. Computer-Aided Multivariate Analysis, 4th ed.,

Atkinson, A. C. [ 19851. Plots, Transformations and Regressions, New York: Oxford University

Chambers, J. M., Cleveland, W. S., Kleiner, B. and Tukey, P. A. [1983]. Graphical Methods

Chatterjee, S. and Hadi, A. S. [1988]. Sensitivity Analysis in Linear Regression, New York:

Cleveland, W. S. [1985]. The Elements of Graphing Data, Monterey, CA: Wadsworth, 155-

Fox, J. and Long, J. S. [1990]. Modern Methods of Data Analysis, Newbury Park, CA: Sage,

Fox, J. [1991]. Regression Diagnostics, Newbury Park, CA: Sage, 21-39.

Lewis-Beck, M. S. [1980]. Applied Regression: An Introduction, Newbury Park, CA: Sage.

Mickey, R. M., Dunn, 0. J. and Clark, V. A. [2004]. Applied Statistics: Analysis of Variance

vanBelle, G., Fisher, L. D., Heagerty, P. J. andLumley, T. [2004]. Biostatistics: AMethodology

Boca Raton, FL: Chapman & HaWCRC, 85-1 18.

Press.

for Data Analysis, Belmont, CA: Wadsworth, 75-124.

Wiley-Interscience, 71-1 82.

191.

257-29 1.

and Regression, 3rd ed., New York: Wiley, 251-255, and 278-284.

for the Health Sciences, New York: Wiley-Interscience, 297-304.