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# Statistic Questions: sample property crime and median income

1. William used a sample of 68 U.S. cities to estimate the relationship between Crime (annual property crimes per 100,000 persons) and Income (median income per capita). His estimated regression equation was Crime = 428 + .050 Income. Assuming that b1 is significant, if Income decreases by 1000 we would predict that Crime will

A) increase by 428
B) increase by 50
C) increase by 500
D) none of the above are correct

2. Bivariate prediction intervals for Y are narrowest when

A) the mean of X is near the mean of Y.
B) the value of X is near the mean of X.
C) the mean of X differs greatly from the mean of Y.
D) the mean of X is small

3. When comparing the 90% prediction and confidence intervals for a given regression analysis

A) the prediction interval is wider than the confidence interval.
B) the prediction interval is narrower than the confidence interval
C) there is no difference between the size of the prediction and confidence intervals
D) None of the above

4. Which is not true of the coefficient of determination?

A) It is the square of the coefficient of correlation.
B) It is negative when there is an inverse relationship between X and Y.
C) It reports the percent of the variation in Y explained by X.
D) It is based on sum of squares (SSR, SSE, and SS total).

5. If X2 is a binary predictor in Y = &#61538;0 + &#61538;1 X1 + &#61538;2 X2 then which statement is most nearly correct?

A) X2 = 1 should represent the most desirable condition.
B) if &#61538;2 = 423.72 then X2 is a key predictor.
C) X2 may shift the estimated equation by a constant amount &#61538;2.
D) None of the above.

6. Using a sample of 63 observations, two variables X1 and X2 are regressed against a dependent variable Y yielding the fitted regression equation = 76.40 &#61485; 6.388x1 + .870x2. The standard error of b1 is 2.453. In a two-tailed test of the hypothesis that &#61538;1 = 0 at &#61537; = .05, we would conclude that

A) there is a significant direct relationship between X1 and Y.
B) there is a significant inverse relationship between X1 and Y.
C) there is insufficient statistical evidence to say that a relationship exists between X1
and Y
D) there is too much Type II error risk to conclude anything about the relationship.

7. A multiple regression analysis involving two independent variables yielded the following information: n = 12, SS(Total) = 798.011, SS(Regression Model) = 738.00. The multiple correlation coefficient is:

A) 60.011
B) 55.3389
C) 0.925
D) 0.962

8. Based on the following regression ANOVA table, the R2 is
ANOVA
Source df SS MS F
Regression 4 1793.23561 448.3089 7.485401
Risidual 45 2695.09959 59.8011
Total 49

A) 0.6005
B) 0.1336
C) 0.3995