The accompanying data on x = U.S. population (millions) and y = crime index (millions) appeared in the article “The Normal Distribution of Crime” (Journal of Police Science and Administration [1975]: 312–318). The author comments that “The simple linear regression analysis remains one of the most useful tools for crime prediction.” When observations are made sequentially in time, the residuals or standardized residuals should be plotted in time order (that is, first the one for time t = 1 (1963 here), then the one for time t = 2, and so on). Notice that here x increases with time, so an equivalent plot is of residuals or standardized residuals versus x. Using ŷ = 47.26 + .260x, calculate the residuals and plot the (x, residual) pairs. Does the plot exhibit a pattern that casts doubt on the appropriateness of the simple linear regression model? Explain.

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Year 1963 1964 188.5 2.26 y Year 1969 1970 1971 1972 201.9 203.2 206.3 208.2 4.99 5.57 6.00 5.89 X 1965 1966 191.3 193.8 195.9 2.60 2.78 3.24 y 1967 1968 197.9 199.9 3.80 4.47 1973 209.9 8.64