MTH302

1. If the mean of X is 25 and the mean of Y is 25, and XY = 2, then find the value of X when Y = 130:

a) 1/65 b) 1/24 c) 20 d) 1/45

2. Given the two regression lines:

8Y = 4X + 3

Y = 4 - 3X

What are the means of X and Y?

a) X = 23/24, Y = 23/25 b) X = 29/28, Y = 25/28 c) X = 25/28, Y = 24/28 d) X = 23/24, Y = 27/27

3. For a bivariate dataset on (x, y), if the means, standard deviations, and correlation coefficient are given as:

x̄ = 3, ȳ = 2, σx = 9, σy = 8, r = 1

Then, the regression line of y on x is:

a) 9y = 8x - 6 b) 8y = 3x + 7 c) y = 2.4x - 1 d) y = 2.14x - 1

4. If the two regression lines are Y = a + bX and X = c + dY, then the correlation coefficient between X and Y is:

a) ab b)√ad c) ad d) √bd

5. Calculate the rank correlation coefficient from the following data:

Expenditure on advertisement: 10, 15, 14, 25, 14, 14, 20, 22

Profit: 6, 25, 12, 18, 25, 40, 10, 7

a) -0.045 b) -0.024 c) 0.024 d) 0.045

6. Given the dataset:

X = 1, 2, 3, 4

Y = 100, 100, 100, 100

What is the value of the Karl Pearson correlation coefficient?

a) -1 b) 1 c) 0 d) 0.5

7. From the dataset:

X = 20, 20, 20, 20

Y = 10, 20, 30, 40

What is the correlation coefficient?

a) 0 b) 1 c) -1 d) Undefined

8. A statistician computes the Karl Pearson coefficient of correlation (r) between monthly income and monthly expenses for 100 individuals. The value of r is found to be 0.82. Later, he decides to:

1) Express income and expenses in Euros instead of USD.

2) Subtract a fixed amount (1000) from both income and expenses.

What happens to the correlation coefficient after these changes?

a) It will increase. b) It will decrease. c) It will remain the same. d) It will become zero.

9. A company analyzes the relationship between employee work experience (in years) and their productivity score. The Karl Pearson correlation coefficient is found to be -0.85. What is the most appropriate interpretation?

a) As work experience increases, productivity also increases significantly. b) There is no relationship between work experience and productivity. c) As work experience increases, productivity decreases significantly. d) The correlation is weak and does not indicate any meaningful relationship.

10. If X, Y, and Z are random variables each with expectation 10 and variances 1, 4, and 9 respectively, and the correlation coefficients are:

r(X, Y) = 0, r(Y, Z) = r(Z, X) = 1/4

Then, what is Var(3X - Z)?

a) 0 b) 9/4 c) 27/2 d) -9/2

11. For the given set of $X, Y$ values, after shifting the origin as $U = X - 65$ , $V = Y - 32$ , the following results are obtained:

$\sum U = 2, \sum V = 2, \sum U^{2} = 2970, \sum V^{2} = 570, \sum U V = 1178, n = 6$

What is $r (X, Y)$ ?

a) 0.9054 b) 0.8213 c) 0.7661 d) 0.8506

12. The correlation coefficient between $X$ and $Y$ for the following data is:

$X = 1, 3, 4, 5, 7, 8, 10$

$Y = 2, 6, 8, 10, 14, 16, 20$

a) -1 b) 1 c) 0 d) 0.8

13. The coefficient of correlation between two variables $X$ and $Y$ is 0.32. Their covariance is 7.86. The variance of $X$ is 10. The standard deviation of $Y$ series is:

a) 60.33 b) 7.767 c) 9.237 d) 5.436

14. If the angle between the two regression lines is 45°, and the standard deviations of $X$ and $Y$ are 5 and 10 respectively, then the correlation coefficient $r$ is:

a)

\frac{1}{√3}

b)

\frac{1}{√2}

c)

\frac{1}{4}

d)

\frac{1}{3}

15. If the angle $θ$ between two regression lines is given by:

$\tan θ = \frac{2 (1 - r^{2}) \frac{1}{2}}{r (\frac{s_{x}}{s_{y}} + \frac{s_{y}}{s_{x}})}$

and the correlation coefficient $r = 0.8$ , with standard deviations $s_{x} = 4$ and $s_{y} = 5$ , then what is the approximate value of $θ$ ?

a)

26.57 °

b)

30 °

c)

45 °

d)

60 °

MCQ on Mean and Regression

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