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) of a sample of 18 convicted minors.

a. Given that β1 = -0.249 and β0 = 52.273, draw the estimated regression line on the accompanying scatter diagram.
b. How do you account for the fact that Y = 52.273 when IQ = 0, even though the delinquency index goes no higher than 50?
c. Find a 95% confidence interval for the true slope fix using the fact that SY|X = 7.704 and SX = 16.192.
d. Interpret this confidence interval with regard to testing the null hypothesis of zero slope at the α = .05 level.
e. Notice that the convicted minor with IQ = 134 and DI = 39.6 appears to be quite out of place in the data. Decide whether this outlier has any effect on your estimate of the IQ-DI relationship by looking at the graph for the fitted line obtained when the outlier is omitted. (β0 = 70.846 and β1 = -0.444 when the outlier is removed.)
f. Test the null hypothesis of zero slope when the outlier is removed, given that Sy|x = 4.933, Sx = 14.693, and n = 17. (Use α = .05.)
g. For these data, would you conclude that the delinquency index decreases as IQ increases?

DI (Y) IQ(X) | DI (Y) IQ(X) 26.20 110 33.00 89 17.50 102 2525 98 2030 110 3190 98 21.10 122 22.70 119 10.70 120 22.10 18.60 92 116 35.50 5 38.00 73 30.00 19.70 104 41.10 82 3960 134 25.15 114 90 30 0 70 110 130 1Q 00)