To Exam Info

Final Exam Review Questions

Sample Multiple Choice Questions

1. What does the Greek letter θ denote in statistics?
   
   1. An arbitrary population parameter
   2. An inflection point of the population
   3. The population median
   4. The population standard deviation
   
   
2. A random variable x has a normal distribution with mean 100 and SD=20. What is the probability that x is greater than 130?
   a. 0.000     b. 0.067     c. 0.310     d. 0.933
    
3. A random variable x has a normal distribution with mean 100 and SD=20. What is the probability that x is equal to 87?
   a. 0.000     b. 0.067     c. 0.130     d. 0.933
    
4. A dataset has 5 observations. Find the largest normal score using Van der Waerden's method.
   a. 0.17     b. 0.20     c. 0.97     d. 1.00
    
5. A bivariate dataset has these univariate statistics:
   
   x = 300    s_x = 75    y = 100    s_y = 25    r = 0.6
   What is the regression line?
   a. y = 0.2x - 60    b. y = 0.2x + 40    c. y = 0.6x - 100    d. y = 0.6x + 160
    
6. If the regression equation is y = β₀ + β₁ x₁ + β₂ x₂, where the estimated beta values are β₀ = 3, β₁ = 1, and β₂ = 4, what is the predicted value y^ if x₁ = 10 and x₂ = 15?
   a. 50    b. 73    b. 220    b. 350
    
7. If (X^T X)^-1 is defined as
   

     T  -1  [ 4.0  0.5   0.0 ]
   (X X)  = [ 0.5  3.0  -0.2 ]
            [ 0.0 -0.2   5.0 ]
   

   for the regression equation in Question 6, what is the standard error of β₂^ if n = 18 and SSE = 3.5?
   a. 0.435    b. 0.489    c. 1.080    d. 7.826
    
8. If the estimated parameter value is 5.00 with standard error 1.00, find a 99% confidence interval for the true parameter value if DFE = 17.
   a. (-1.96, 1.96)   b. (3.00, 7.00)   c. (2.43, 7.57)    d. (2.10, 7.90)
    
9. For the hat matrix H = X(X^T X)^-1 X^T, which of the following is equal to H?
   a. H²    b. H^T    c. (H^T)²    d. I - H
    
10. For a regression model with three independent variables, n = 19, SSM = 356.3, and SSE = 84.33 is the overall F-test significant at the 0.05 level; at the 0.01 level?
    a. no; no      b. yes; no      c. yes; no      d. yes; yes
     
11. Which type of variable can only take on values 0 and 1?
    a. Categorical     b. Dummy     c. Exogenous     d. Independent
     
12. The regression fallacy arises because
    
    1. 0 < r < 1
    2. s_x and s_y for a dataset are usually non-zero.
    3. Just because x and y are correlated does not mean that x causes y.
    4. The regression line is different than the standard deviation line defined by
       
       y - y = (s_y/s_x)(x - x)

Sample Short Answer Questions

1. Be able to answer questions about a dataset, given the SAS or R output.  This question will be similar to the homework projects.
    
2. Find the matrix normal equation for regression using SAS output.
    
3. What are some of the popular transforms that can be used on a regression model. When would you use them?

Sample Short Essay Questions

1. Explain the differences and similarities between these methods for independent variable selection: maximum R-squared, forward selection, backward selection, stepwise selection.
    
2. Explain the difference between a confidence interval and a prediction interval for y.
    
3. Explain the differences and similarities between classical one-way ANOVA and the independent two-sample t-test.