Download BSTAT 5325 – Exam 2 – Summer, 2010 – White Exam

BSTAT 5325 – Exam 2 – Summer, 2010 – White Exam - Printed Name_______________________
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7. Assume  = 0.05 and 95% confidence unless told otherwise.
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1. Another name for “the standard error of estimate” is
a. George
b. the standard deviation of the Y values for any given value of X
c. the Mean Squared Average
d. the margin of error of the slope
2. You assume that in Analysis of Variance that you have same variance, independent random samples
and normal distributions. What new assumption has been added in simple linear regression?
a. simple equations to solve
b. linearity
c. hypothesis testing
d. confidence intervals
3. Least squares estimates of the population slope and intercept are calculated from the sample in
order to
a. minimize the squared differences between the actual values of Y and the predicted values of Y.
b. sell computers (Hint: do not buy into this answer)
c. minimize the squared value of the sample slope and sample intercept.
d. minimize the coefficient of determination
4. In a simple linear regression analysis, you find that your sample size is 10 and the standard error of
the sample slope (Sb1 ) is 0.05. With 95% confidence what is the largest error you expect in the estimate
of the population slope?
a. 0.05
b. 0.1153
c. 0.0980
d. none of the other answers are correct
5. If you have a first-order model and see a U shaped set of points in a residual plot, you should
consider adding a _____________ to the model
a. another intercept
b. product of two independent variables
c. fix to the violation of equal variance
d. square of one of independent variables
6. You are examining the effect of the length of an exam and the temperature of the room on the exam
grade. If you feel that temperature would not have as much effect on the exam for short exams than for
long exams, you would use a(n):
a. simple linear model
b. second-order (quadratic) model
c. first-order model
d. interaction model
7. In a ________________ relationship all the points fall on a line while in a _______________
relationship the points just on average fall on the line. The answers below are the same order as the
blanks.
a. quadratic, linear
b. mathematical, statistical
c. geometric, non-geometric
d. mean, standard deviation
8. If Y = the rate of return of a stock and X = the Standard and Poor’s 500 index, what would be an
interpretation of the sample slope of 1.5?
a. for each point increase in the S&P 500, we estimate that the average rate of return of the stock will be
1.5 points.
b. when the S&P 500 is zero, we estimate that the average rate of return of the stock will increase by 1.5
points.
c. for each point increase in the S&P 500, we estimate that the average rate of return of the stock will
increase by 1.5 points.
d. 150% of the variability in the stock is associated with variability in the S&P 500
9. Warning: Algebra problem. If you have the following model: the predicted value of Y = 60 + 4X1 + 2X2
– 3X1X2, what would be the effect of X2 when X1=5? “Holding X1 equal to 5, for each one point increase in
X2, the predicted value of Y
a. decreases by 13
b. decreases by 3
c. increases by 2
d. is 75
10. In the material we have covered in my notes, both simple and multiple regression all of the
techniques in the answers below except for ______
a. t-tests
b. margins of error
c. coefficients of determination
d. F-tests
11. In a second order model 0+1X+2X2 where Y=employee productivity, X=number of jobs coming
into the shop, the interpretation of the slope 1 is
a. none of the other answers are correct
b. Holding the number of jobs constant, this would be the change in the average employee productivity
when the square of the number of jobs increases by one.
c. Holding the productivity constant, this would be the change in the average employee productivity
when the number of jobs increases by one.
d. The change in the average employee productivity when the number of jobs increases by one.
12. “For each one unit increase in X, the mean value of Y for all values in the population increases by 6.”
This is a definition of the term symbolized by
a.  1
b.  0
c. b1
d. R2
13. Why do we assume that the variation of Y for fixed values of the independent variables is the same
regardless of the values of the independent variables?
a. needed for normality
b. so that the model stays linear
c. only if the sample is random and independent
d. simplicity
14. You decide to use a quadratic model: 0+1(salt)+ 2(salt)2 for estimating the average taste test of a
food product. When calculating the largest error you would expect in estimates, what degrees of
freedom would use for the t-table value? You are given that n=50.
a. 49
b. 48
c. none of the other answers are correct
d. 47
15. In simple linear regression, you are given that your sample size is 20, the sample slope (b1) is 1.5,
and the standard error of the sample slope (Sb1 ) is 0.05. If you are trying to support that there is a
positive relationship between the two variables, what would be your conclusion?
a. We cannot say that for each one point increase in X, the mean value of Y does increase.
b. We can say that for each one point increase in Y, the mean value of X does decrease.
c. We can say that the mean value of Y is above 1.5.
d. We can say that for each one point increase in X, the mean value of Y does increase.
16. You wish to show that a multiple linear regression model can be used to predict the values of the
dependent variable. What test would you use to show this?
a. chi-square test
b. t-test
c. the N test
d. F-test
17. In which of the following do you have to add the phrase “Holding all other variables constant”?
a. the value of the sample standard deviation
b. the conclusion of the F-test in multiple regression
c. the conclusion for a t-test in multiple regression.
d. the conclusion for a t-test in simple linear regression.
18. Suppose all assumptions in simple linear regression are being met. In which of the two plots
(residual plot or normal probability plot) would you expect to see a straight line of points that start in
the bottom left of the plot and go to the top right of the plot?
a. normality plot
b. residual plot
c. both
d. neither
19. The standard errors we covered in regression are still composed of measures of variation and
knowledge. However knowledge now includes
a. a random sample from a normal distribution
b. knowledge about the independent variables
c. a t with n-1 degrees of freedom
d. the same thing as before. It is just a function of the number of observations.
20. Given the least squares estimates of the intercept and slope to be 12 and 1.5, respectively, what
would be the predicted value of Y for an X value of 10?
a. 13.5
b. 27
c. 121.5
d. none of the other answers are correct
21. In a two independent variable first order model you find that the coefficient of determination is
0.65. The interpretation of the value 0.65 is
a. Using the first order model, 65% of the sample variability in Y is associated with the variation in the
one of the independent variables while holding the other one constant.
b. There is a typical error of 0.65 when trying to predict the value of Y using the first-order model.
c. Using the first order model, 65% of the sample variability in Y is associated with the variation in the
two independent variables.
d. the assumptions are being violated since the value is so small.
22. What would be the rejection region for the F-test of an interaction model assuming only two
independent variables? You are given that n=40. Reject Ho if the test statistic value is
a. greater than F with 2 and 37 degrees of freedom
b. greater than a t with 36 degrees of freedom
c. greater than F with 3 and 36 degrees of freedom
d. greater than F with 1 and 36 degrees of freedom
23. If you see that all the points on a graph are falling very close to a straight line, then you would
expect the _________ to be large.
a. the standard error of the estimate of the slope
b. the value of the population slope
c. the coefficient of determination
d. residuals
24. Suppose that in a first-order model with 2 independent variables that you are trying to show that
there is a negative effect of X2 (H1: 2 < 0). Using b2 and its standard error, you find a t-test value of
11.948. What would be your conclusion? After holding X1 constant, we
a. can say that X2 has a negative effect on the mean of Y.
b. 11% of the sample variation in Y is associated with variation in X2.
c. cannot say that X2 has a negative effect on the mean of Y.
d. the population intercept could be zero.
25. For a given a value of X, the standard error for predicting the value of Y for one observation is
__________ than the standard error for estimating the mean value of Y for all observations.
a. smaller
b. the same
c. larger
d. not enough information to determine which is larger
Question
1
2
3
4
5
6
7
8
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10
11
KEY
B
B
A
B
D
D
B
C
A
D
B
12
13
14
15
16
17
18
19
20
21
22
23
A
D
D
D
D
C
A
B
B
C
C
C
24 C
25 C