1. A sociologist assigned to a correctional institution was interested in studying
the relationship between intelligence and delinquency. A delinquency index
(ranging from 0 to 50) was formulated to account for both the severity and
the frequency of crimes committed, while intelligence was measured by IQ. The
following table displays the delinquency index (DI) and IQ of a sample of 18
convicted minors.
DI 26.2 33.0 17.5 25.25 20.3 31.9 21.1 22.7 10.7
IQ 110 89 102 98 110 98 122 119 120
DI 22.1 18.6 35.5 38.0 30.0 19.7 41.1 39.6 25.15
IQ 92 116 85 73 90 104 82 134 114
(a) Plot a scatter diagram for DI versus IQ. Determine the least-square estimate
of the regression line when DI regressed on IQ. Sketch the estimated line on the
scatter plot.
(b) Notice that the convicted minor with IQ=134 and DI=39.6 appears to be
quite out of place in the data. Determine the least-square estimate of the
regression line when the outlier is removed. Sketch the estimated line on the
scatter plot. By looking at the graph for the fitted line obtained when the
outlier is omitted, Decide whether this outlier has any effect on your estimation
of IQ-DI relationship.
(c) For these data, would you conclude that the delinquency index decreases as
IQ increases?
(d) Is it justifiable to predict DI for IQ=0 from the fitted regression line?(Note
that the delinquency index goes no higher than 50.)
2. The accompanying table gives the dry weights (Y) of 11 chick embryos
ranging in age from 6 to 16 days (X).
Age (X)(days) 6 7 8 9 10 11
Dry Weight (Y) 0.029 0.052 0.079 0.125 0.181 0.261
Age (X)(days) 12 13 14 15 16
Dry Weight (Y) 0.425 0.738 1.13 1.882 2.812
1
Docsity.com
