وَأَحْصَىٰ كُلَّ شَيْءٍ عَدَدًا
"And He has enumerated everything in numbers." (Allah perfectly counts and knows the exact measure of all creations).
Q1. The study of the relationship between variables
for prediction and estimation is called:
A. Regression analysis ✓ Correct Answer
B. Time series analysis
C. Correlation analysis
D. All of these
Explanation: Regression analysis specifically studies relationships
between variables in order to predict or estimate one from another.
Q2. The variable that forms the basis of estimation
or prediction is the:
A. Regressand
B. Regressor ✓ Correct Answer
C. Dependent variable
D. Explained variable
Explanation: The regressor is the variable used as the basis for
predicting or estimating another variable — the independent variable.
Q3. The regressand is also called the:
A. Dependent variable ✓ Correct Answer
B. Independent variable
C. Explanatory variable
D. Regressor
Explanation: Regressand and dependent variable are two names for the
same thing — the variable being predicted.
Q4. The regressor is also called the:
A. Independent variable
B. Controlled variable
C. Explanatory variable
D. All of these ✓ Correct Answer
Explanation: Independent, controlled, and explanatory variable are all
alternate names for the regressor.
Q5. A relation where the dependent variable is
uniquely determined by the value of the independent variable is called a:
A. Functional relation
B. Mathematical relation
C. Deterministic relation
D. All of these ✓ Correct Answer
Explanation: A functional, mathematical, and deterministic relation
all describe the same idea — an exact, unique determination of Y from X.
Q6. A relation where all values fall directly on the
line is called a:
A. Functional relation
B. Statistical relation
C. Mathematical relation
D. Both (a) and (c) ✓ Correct Answer
Explanation: When every point lies exactly on the line (no scatter),
this describes both a functional and mathematical relation.
Q7. A relation where the dependent variable is not
uniquely determined is called a:
A. Functional relation
B. Mathematical relation
C. Deterministic relation
D. Statistical relation ✓ Correct Answer
Explanation: When Y isn't exactly fixed by X (some scatter/randomness
exists), this describes a statistical relation.
Q8. A relation where observations don't fall directly
on the line or curve is called a:
A. Statistical relation
B. Regression relation
C. Probabilistic relation
D. All of these ✓ Correct Answer
Explanation: Statistical, regression, and probabilistic relation are
all terms describing this scattered, non-exact relationship.
Q9. The relationship between yield and quantity of
fertilizer is:
A. Functional
B. Statistical ✓ Correct Answer
C. Deterministic relation
D. All of these
Explanation: Since yield doesn't depend purely and exactly on
fertilizer amount (other factors add randomness), this is a statistical
relationship.
Q10. The height of a son related to the height of his
father is a:
A. Probabilistic relation
B. Statistical relation
C. Regression relation
D. All of these ✓ Correct Answer
Explanation: This relationship is scattered rather than exact, making
it simultaneously probabilistic, statistical, and a regression relation.
Q11. Which of the following is true for a
mathematical model?
A. Contains the random error
B. Doesn't contain the
random error ✓ Correct Answer
C. Contains residuals
D. Comes with an error term
Explanation: A mathematical model represents an exact relationship, so
it has no random error term.
Q12. A statistical model:
A. Contains the random
error ✓ Correct Answer
B. Doesn't contain the random
error
C. Shows an exact relationship
D. None
Explanation: Unlike a mathematical model, a statistical model
explicitly includes a random error term to account for scatter.
Q13. The method of estimating an average relationship
between variables is called:
A. Regression analysis ✓ Correct Answer
B. Time series analysis
C. Correlation analysis
D. Computer analysis
Explanation: Regression analysis is specifically the technique used to
estimate the average relationship between variables.
Q14. The best fitting curve has a sum of squares of
residuals that is:
A. Minimum ✓ Correct Answer
B. Maximum
C. Largest
D. None
Explanation: The least squares method finds the best-fitting curve by
minimizing the sum of squared residuals.
Q15. The errors eᵢ in a regression model are often
called:
A. Residuals
B. Deviations
C. Prediction errors
D. All of these ✓ Correct Answer
Explanation: Residuals, deviations, and prediction errors are all
common names for the eᵢ terms in a regression model.
Q16. Error arising from a lack of precision in
measuring variables is called:
A. Measurement error ✓ Correct Answer
B. Sampling error
C. Specification error
D. Random error
Explanation: Imprecise measurement of variables directly causes what
is called measurement error.
Q17. Error arising from the omission of one or more
relevant independent variables is called:
A. Measurement error
B. Sampling error
C. Specification error ✓ Correct Answer
D. Random error
Explanation: Leaving out relevant explanatory variables from a model
is known as specification error.
Q18. A simple linear regression model contains:
A. Only one variable
B. Two variables ✓ Correct Answer
C. More than two variables
D. Both (a) and (b)
Explanation: A simple linear regression model relates exactly two
variables — one dependent and one independent.
Q19. One regression line is horizontal and the other
is vertical when:
A. r = 0 ✓ Correct Answer
B. r < 0
C. r > 0
D. r = 1
Explanation: When there's no linear relationship (r=0), the two
regression lines become perpendicular — one horizontal, one vertical.
Q20. Which of these is a parameter of the linear
regression model?
A. α, β
B. σ²
C. μY|X
D. All of these ✓ Correct Answer
Explanation: The linear regression model includes several parameters:
the intercept/slope (α, β), the error variance (σ²), and the conditional mean
(μY|X).
Q21. The least squares regression line minimizes the:
A. Calculation mistakes
B. Sum of squares of
errors ✓ Correct Answer
C. Spelling mistakes
D. None
Explanation: By definition, the least squares method finds the line
that minimizes the sum of squared errors.
Q22. The change in the dependent variable Y for a
unit change in the independent variable x is measured by:
A. b_yx ✓ Correct Answer
B. a_ye
C. r
D. None
Explanation: The regression coefficient b_yx represents exactly this —
the change in Y per unit change in x.
Q23. The regression coefficient is independent of:
A. Origin ✓ Correct Answer
B. Scale
C. Both (a) and (b)
D. Unit of measurement
Explanation: Regression coefficients remain unchanged when data is
shifted (origin), but do change when data is rescaled.
Q24. Two regression coefficients always have:
A. Opposite signs
B. The same sign ✓ Correct Answer
C. No sign
D. None
Explanation: Since both regression coefficients share the sign of the
covariance between X and Y, they always match in sign.
Q25. If b_yx is greater than one, then b_xy is:
A. Less than one ✓ Correct Answer
B. Also greater than one
C. Equal to one
D. None
Explanation: Since b_yx × b_xy = r² ≤ 1, if b_yx exceeds 1, b_xy must
be less than 1 to keep their product within bounds.
Q26. If b_yx = 1.34, then b_xy would be:
A. -1.34
B. 0.50 ✓ Correct Answer
C. 1.34
D. -1.00
Explanation: Since b_yx and b_xy must have the same sign and their
product can't exceed 1, only 0.50 (giving product ≈0.67) is consistent — the
others violate this constraint.
Q27. b_yx, b_xy, and S_xy always have:
A. The same sign ✓ Correct Answer
B. Opposite signs
C. No sign
D. Mixed signs (+,+,-)
Explanation: Since all three quantities derive from the same
covariance, they always share the same sign.
Q28. For ŷ = a + bx, Σ(ŷ - ȳ) is always equal to:
A. Zero ✓ Correct Answer
B. Greater than zero
C. More than zero
D. Undefined
Explanation: The sum of deviations of predicted values from their mean
always equals zero, just like for the original data.
Q29. For ŷ = a + bx:
A. Σŷ > Σȳ
B. Σŷ ≠ Σȳ
C. Σŷ = Σȳ ✓ Correct Answer
D. Σŷ < Σȳ
Explanation: The regression line is fitted such that the sum of
predicted values equals the sum of actual values.
Q30. The regression line between X and Y always
passes through the point:
A. (x̄, ȳ) ✓ Correct Answer
B. The origin
C. The x-axis
D. None
Explanation: By construction, the least squares regression line always
passes through the mean point (x̄, ȳ).
Q31. The measure of the linear mutual variability of
two variables is called:
A. Covariance ✓ Correct Answer
B. Skewness
C. Dispersion
D. Central tendency
Explanation: Covariance specifically measures how two variables vary
together (linearly) relative to each other.
Q32. If the variables tend to move in the same
direction, the sign of covariance is:
A. Negative
B. Positive ✓ Correct Answer
C. No sign
D. None
Explanation: When both variables increase or decrease together, their
covariance is positive.
Q33. If the variables tend to move in opposite
directions, the sign of covariance is:
A. Negative ✓ Correct Answer
B. Positive
C. No sign
D. None
Explanation: When one variable increases as the other decreases, their
covariance is negative.
Q34. If X and Y are independent variables, then
Cov(X,Y) =
A. Negative
B. Positive
C. Zero ✓ Correct Answer
D. Non-zero
Explanation: Independent variables show no linear association, so
their covariance is exactly zero.
Q35. If r_xy = -0.84, then r_yx =
A. -0.84 ✓ Correct Answer
B. 0.84
C. 0.42
D. None
Explanation: The correlation coefficient is symmetric — r_xy always
equals r_yx.
Q36. If r_xy = -0.84, and u = -2X, v = 4y, then r_uv
=
A. -0.84
B. 0.84 ✓ Correct Answer
C. 0.42
D. Undefined
Explanation: Correlation's sign flips when the product of the two
scaling constants is negative: here (-2)×(4) = -8 < 0, so r_uv = -r_xy =
0.84.
Q37. The value of the correlation coefficient is
always in the range:
A. 0 to 1
B. -1 to 1 ✓ Correct Answer
C. -1 to 0
D. None
Explanation: Correlation coefficients are always bounded between -1
and +1, inclusive.
Q38. The two regression lines are perpendicular to
each other when:
A. r = 0 ✓ Correct Answer
B. r = 1/3
C. r = -1/2
D. r = ±r
Explanation: With no linear relationship (r=0), the regression lines
become perpendicular to one another.
Q39. The regression lines coincide (become the same
line) if:
A. r = 0
B. r = 1/3
C. r = -1/2
D. r = ±1 ✓ Correct Answer
Explanation: When correlation is perfect (r = ±1), both regression
lines collapse into a single line.
Q40. If two regression lines are ŷ = a + bx and x̂ =
c + dy, then the correlation coefficient between x and y is:
A. √bc
B. √ac
C. √ad
D. √bd ✓ Correct Answer
Explanation: The correlation coefficient equals the geometric mean of
the two regression slopes: r = √(b × d).
Q41. If two regression coefficients are 0.8 and 0.2,
the value of the correlation coefficient is:
A. 0.16
B. -0.16
C. 0.40 ✓ Correct Answer
D. -0.40
Explanation: r = √(b_yx × b_xy) = √(0.8 × 0.2) = √0.16 = 0.40.
Q42. If b_yx = 1.34, then b_xy could be:
A. -0.16
B. 2.43
C. 0.40 ✓ Correct Answer
D. All of these
Explanation: Since b_yx and b_xy must share the same sign and their
product must not exceed 1, only 0.40 (giving ≈0.536) is a consistent value
here.
Q43. The correlation coefficient r is the ___ mean of
the two regression coefficients.
A. Geometric ✓ Correct Answer
B. Arithmetic
C. Harmonic
D. None
Explanation: By definition, r = √(b_yx × b_xy), which is exactly the
geometric mean of the two regression coefficients.
Q44. Which of these is a valid value for a
correlation coefficient?
A. -1.95
B. 1.95
C. 0.95 ✓ Correct Answer
D. None of these
Explanation: Since correlation must lie strictly between -1 and 1,
only 0.95 is a mathematically valid correlation coefficient among these
options.
Q45. r = 0 indicates that the two variables are
linearly:
A. Independent ✓ Correct Answer
B. Dependent
C. Related
D. None
Explanation: A correlation of zero means there's no linear
relationship — the variables are linearly independent (though they might still
be related non-linearly).
Q46. The negative sign of r_xy indicates that X and Y
are:
A. Directly related
B. Inversely related ✓ Correct Answer
C. Moving in the same direction
D. Unrelated
Explanation: A negative correlation coefficient means X and Y move in
opposite directions — they are inversely related.
Q47. If S_xy = 0, then b_yx, b_xy, and r_xy are:
A. Negative
B. Positive
C. Zero ✓ Correct Answer
D. None
Explanation: Since all three quantities are derived directly from S_xy
(covariance), a zero covariance makes all three zero as well.
Q48. The geometric mean of the two regression
coefficients gives the:
A. Correlation
coefficient ✓ Correct Answer
B. Regression coefficient
C. Coefficient of skewness
D. None
Explanation: By definition, √(b_yx × b_xy) equals the correlation
coefficient, r.
Q49. If one of the variables is constant, the
correlation coefficient is:
A. Less than one
B. More than one
C. Equal to one
D. Zero ✓ Correct Answer
Explanation: With no variability in a constant variable, there's no
linear covariation to measure, so the correlation coefficient comes out as
zero.
Q50. Covariance of two variables measured in standard
units is called the:
A. Correlation
coefficient ✓ Correct Answer
B. Regression coefficient
C. Coefficient of skewness
D. None
Explanation: Standardizing covariance (dividing by both standard
deviations) is exactly how the correlation coefficient is defined.
Q51. The magnitude of the correlation coefficient
doesn't change if:
A. The origin is changed
B. The scale is changed
C. Both (a) and (b) ✓ Correct Answer
D. None
Explanation: Correlation is unaffected by shifting (origin) or (for
same-signed) rescaling of the data — it remains the same in magnitude.
Q52. The sign of S_xy, b_xy, b_yx, and r_xy is
always:
A. The same ✓ Correct Answer
B. Opposite
C. Unpredictable
D. Not matched
Explanation: Since b_xy, b_yx, and r_xy are all derived from the
covariance S_xy, they always share the same sign.
Q53. A negative sign of r_xy indicates that X and Y
are related:
A. Inversely ✓ Correct Answer
B. Directly
C. Positively
D. In an unexplained way
Explanation: A negative correlation coefficient means the two
variables are inversely related — as one increases, the other decreases.
Q54. A positive sign of r_xy indicates that X and Y
are related:
A. Inversely
B. Directly ✓ Correct Answer
C. Negatively
D. In an unexplained way
Explanation: A positive correlation coefficient means the two
variables are directly related — they move in the same direction.
Q55. A positive correlation indicates that as one
variable increases, the other:
A. Decreases
B. Increases ✓ Correct Answer
C. Stays unchanged
D. None
Explanation: Positive correlation means both variables move together —
as one goes up, so does the other.
Q56. A negative correlation indicates that as one
variable increases, the other:
A. Decreases ✓ Correct Answer
B. Increases
C. Stays unchanged
D. None
Explanation: Negative correlation means the variables move oppositely
— as one increases, the other decreases.
Q57. In correlation analysis, the two regression
lines always intersect at:
A. The y-intercept
B. The origin
C. (x̄, ȳ) ✓ Correct Answer
D. None
Explanation: Since both regression lines pass through the mean point,
that's exactly where they intersect.
Q58. The slope of the regression line is also known
as the:
A. Regression coefficient ✓ Correct Answer
B. Y-intercept
C. Ordinates
D. None
Explanation: The slope of a regression line is precisely what's called
the regression coefficient.
Q59. If the two regression coefficients are negative,
then the correlation coefficient is:
A. Positive
B. Negative ✓ Correct Answer
C. Without sign
D. Does not exist
Explanation: Since r = √(b_yx × b_xy), and both coefficients share
sign with r, negative regression coefficients mean a negative correlation
coefficient.
Q60. If the two regression coefficients are positive,
then the correlation coefficient is:
A. Positive ✓ Correct Answer
B. Negative
C. Without sign
D. Does not exist
Explanation: Since both regression coefficients and r always share the
same sign, positive regression coefficients mean a positive correlation
coefficient.
Q61. The two regression lines are at right angles
when the correlation coefficient is:
A. Zero ✓ Correct Answer
B. Positive
C. Negative
D. None
Explanation: With zero correlation, there's no linear association,
causing the two regression lines to become perpendicular.
Q62. r = 1 indicates:
A. Perfect positive
correlation ✓ Correct Answer
B. Perfect negative correlation
C. Non-sense correlation
D. No correlation
Explanation: A correlation coefficient of exactly +1 represents
perfect positive correlation between the variables.
Q63. The correlation coefficient r is:
A. Independent of the unit of
measurement
B. Independent of origin
C. Not independent of scale
D. Both (a) and (b) ✓ Correct Answer
Explanation: Correlation is a pure, unit-less number that doesn't
change with the unit of measurement or a shift in origin.
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