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Test 2. Right answers.
1. In a linear regression model the residual variance is 25 and the variance explained by the regression is 75, it means that:
Selected Answer: (^) a. The determination coefficient is 0.75.
2. If the linear correlation coefficient between two variables is 1.01, then:
Selected Answer: c. This situation can not happen.
3. If two variables are independent, then:
Selected Answer: (^) c. Their covariance is always zero
4. The marginal distribution for X:
Selected Answer: b. Is the distribution of X independently any value Y takes.
5.In a double entry frequency table for two variables X and Y, with all the marginal
distributions different from zero, but with some value nij=0, could X and Y be independent?
Selected Answer:a. No
- A bidimensional distribution allows to observe:
Selected Answer: b. Two characteristic of each element in a population.
7.If the variables X and Y are independent, then for every i and j holds that:
Selected Answer: b. ni·*n·j/N=nij
8. If we estimate Y* = 20 X + 8, then, an increase in one unit of X would lead to an
increase in Y equal to:
Selected Answer:c. 20
9. The two regressions lines of a bidimensional variable:
Selected Answer: a. Nor a) nor b)
10. If the regression line between Y and X is a decreasing line, then we can say:
Selected Answer: b. The linear correlation coefficient is negative.
11. In a double entry correlation table for the bidimensional variable (X,Y)
Selected Answer: X and Y are independent if fi·*f·j=fij
12. A bidimensional distribution allows to observe:
Selected Answer: b. Two characteristic of each element in a population
13. Two independent variables:
Selected Answer: c. Always have zero covariance.
14. If the regression line of Y on X is y=10x+2 and Sxy=40, then S^2x is:
Selected Answer: a. 4
15. If the regression lines Y|X and X|Y never cut, it would mean that:
Selected Answer: b. This can never happen.
16. If two variables are linearly related and their covariance is 3, then the linear
relationship is:
Selected Answer: (^) c. Direct.
17. If the linear relationship between two variables X and Y is perfect:
Selected Answer: b. The determination coefficient is 1.
18. Two variables with zero covariance means that:
Selected Answer: a. We can not say anything about the Independence between these variables.
19. The marginal distribution for X:
Selected Answer: b. Is the distribution of X independently any value Y takes.
20. Let b and b’ the regression coefficients for the linear regressions for Y|X and
X|Y respectively, then:
Selected Answer: (^) b. b and b’ have the same sign
21. In a linear regression model Y|X, the variance of Y is 10, the variance of X is 5
and the residual variance is 1. Which is the right answer?
Selected Answer: (^) a. The determination coefficient is 0.9.
22. The representativity of the regression line increases when:
Selected Answer: (^) b. The residual variance decreases.
23. The ratio between the explained variance by the regression and the total
variance receives the name:
Selected Answer: (^) b. Determination coefficient.
24. Let X and Y be two independent variables. We define Z = 5Y. Then:
Selected Answer: c. X and Z are independent.
25.The curve through the points (xi, y|xi) of a bidimensional distribution (X,Y) is:
Selected Answer: c. The general regression line Y|X
26. in correlation coefficient is equal to 1, it means that:
Selected Answer: b. The relationship between the variables is exactly linear and direct.
27. In the linear regression model, the variance of the dependent variable is
decomposed by:
Selected Answer:
c. The sum of the variance explained by the regression plus the residual variance.
42. If we know that the determination coefficient is 0.81, then the linear correlation
coefficient is:
Selected Answer: (^) a. 0.9 or – 0.
43. If two variables are independent, then:
Selected Answer: (^) a. Nor a) nor b).
44.If the linear regression lines associated to a bidimensional variable (X, Y) are:
2x + 3y -8 =0 and 8x+6y+9=0. Then R^2 is
Selected Answer: (^) a. 1/
45. The general regression line Y|X is defines as:
Selected Answer: b. The curve through the points (xi ; Y|x=xi)
46. Let b be the regression coefficient for the regression line , and let b’ the
regression coefficient for the regression line , both positive. In this case, slopes for
those models are b y 1/b' respectively, then:
Selected Answer: a. always b ≤1/b'
47. If the linear relationship between two variables X and Y is perfect:
Selected Answer: a. The determination coefficient is 1.
48. The determination and linear correlation between two variables X and Y:
Selected Answer: a. They are equal some times.
49. If yi* are the values estimated by the regression line Y|X for the values xi, then
the residual variances is defined by:
Selected Answer: 1/n sumatorio (yi-yi*)^
50. If we know that the linear correlation coefficient is -1, it means that:
Selected Answer: (^) b. There is a perfect correlation between the variables.
51. If Sxy=69, sumatorio xiyi=1344 y=-7 and N=28 ten x is:
Selected Answer:b. 3
52. In a bidimensional variable, its central moment of order 1x1 defines:
Selected Answer: (^) c. The covariance.
53. Two variables X and Y are independent if:
Selected Answer: (^) b. Their relative conditioned distributions are equal
54. A determination coefficient equal to 0.9, means that:
Selected Answer:
a. 90 % of the total variance of Y is explained by the linear relationship between X and Y.
55. If Y=a+bX and X=a’+b’Y are the regression lines for X and Y, and b>1, then:
Selected Answer: (^) b. b’<1.
56. The linear regression Y|X, verifies that:
Selected Answer:
a. The variance of Y is equal to the variance explained by the regression and the residual variance.
57. In a bidimensional variable, the values of one of the variables is almost half the
values of the other. Then the linear correlation coefficient between them is:
Selected Answer: (^) a. Positive.
58. Given the information of the bidimensional variable (X, Y), U=(X-5)/2, and
V=(Y+6)/3. Which is the value of the regression coefficient from Y over X?
Selected Answer: 3Suv/2Su^
59. If Y=a+bX and X=a’+b’Y are the two regression lines between X and Y, and
b>1, then:
Selected Answer: (^) c. b’<1.
60. If the linear correlation coefficient between two variables X and Y is zero, then:
Selected Answer: b. There is nothing we can say about the dependence relationship between X and Y.
61. In the regression models Y = a + bX and X = a’ + b’Y, the product of their
respective regression coefficients b and b’ is:
Selected Answer: b. The determination coeffcient between X and Y.
62. A determination coefficient equal to 0.9, means that:
Selected Answer:
c. 90 % of the total variance of Y is explained by the linear relationship between X and Y
