X5 014 0 35 033 085

population number of known offenses per thousand of

X2 = percentage of male inhabitants

X3 = percentage of total inhabitants who are foreign-born males X4 = number of children under 5 years of age per thousand married women between ages 15 and 44 years X5 = church membership, number of church members 13 years of age and over per 100 of total population 13 years of age and over; Sj to S5 are the sample standard deviations of variables Y through X5 and R is the correlation matrix a. Treating Y as the dependent variable, obtain the regression of Y on the four X variables and interpret the estimated regression.

*W. F. Ogburn, "Factors in the Variation of Crime among Cities,'' Journal of American Statistical Association, vol. 30, 1935, p. 12.

952 APPENDIX C: THE MATRIX APPROACH TO LINEAR REGRESSION MODEL

c. Obtain R2 and test the hypothesis that all partial slope coefficients are simultaneously equal to zero.

C.9. The following table gives data on output and total cost of production of a commodity in the short run. (See Example 7.4.)

Output

Total cost, $

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