Match the appropriate distribution to each of the descriptions below. Note: Some items may have more than one correct answer, but you only have to provide one of the correct ones. Also, some distributions may be used more than once while others may not be used at all.

If the data follow a multivariate normal distribution, an informal guideline is that an outlier is a point with a Mahalanobis-distance greater than 2.

When deciding between two models, select the one with the higher adjus­ted R2 measure.

(2+6+2+6=16 pts) A multiple linear regression model was built, based on observations from crime rate data (measured as number of offenses per million population) and a variety of variables by US state (N=47). The results are shown below (“DV” means “dummy variable”).   Mean Value Standard Deviation Estimated Coefficient Standard Error of Coefficient t-value p-value VIF Intercept     -278.67966 81.34388 -3.426 0.00146   Young males (number of males ages 18-24 per 1000 males) 138.6 12.57 0.75550 0.31876 2.370 0.02282 2.065 Expenditure on police ($ per capita) 85.0 29.72 0.72833 0.17743 4.105 0.00020 3.578 More males than females (DV) 0.1915 0.40 7.29241 7.92895 0.920 0.36337 1.280 State pop. (in hundred thousands) 36.62 38.07 -0.07602 0.10385 -0.732 0.46854 2.012 Mature unemployment (number of unemp. males aged 35-39 per 1000 males) 33.98 8.45 0.20338 0.36417 0.558 0.57971 1.217 Wage (median weekly wage, US$) 594.6 96.49 0.20872 0.08265 2.525 0.01573 8.185 Poverty rate (number of families below half the median wage per 1000) 193.0 39.90 0.51394 0.16425 3.129 0.00331 5.527   The ANOVA table is shown below. Source of variation Sum of squares Degrees of freedom Mean square F0 Regression 24462 7 3494.57 9.777 Error or residual 13940 39 357.44 Total 38402 46 a.  What is the R2 for this model? What does it mean in plain English? b.  What do the coefficient and p-value of “Expenditure on police” mean in plain English, for a state with a population of 1 million? Is the coefficient reasonable?  If not, why not, and what should be done about it? c.  For the model specified as shown, should we worry about collinearity? Why or why not? d. For a state with a crime rate of 120 offenses per million population and an expenditure on police of $104 per capita, what is the point elasticity of crime rate with respect to expenditure on police? Is this inelastic, unit elastic, or elastic? What does the number mean in plain English? Answer the same questions for a state with a crime rate of 80 offenses per million population and an expenditure on police of $120 per capita.

Which of the following correctly describes how light will be affected as it tries to escape from the innermost orbits of a black hole?

The next two questions are designed to start you thinking about ionic bonds, a complicated subject, but we can make a few rough decisions and calculations here.

Outliers in a regression model may change the sign of a cor­relation or regression coefficient.

This is a reason for A and B to have a statistically insignificant correlation (association), even though there actually is a causal relationship between them: The relationship between “A” & B is nonlinear.

It is impossible for any object to have a charge of 7.5 e.

The direction of the current I in a metal wire is the same as the direction of the internal electric field in the wire but it is opposite to the direction the electrons are moving.