,MATH 110 Module 9 | Practice Q&A | 2026/2027 | Statistics | Portage
Learning | 100% PASS
1. The correlation coefficient r measures:
A) The slope of the regression line
B) The strength and direction of the linear relationship between two variables
C) The proportion of variance explained
D) The predicted value of y
Correct Answer: The strength and direction of the linear relationship between
two variables
Rationale: The correlation coefficient r measures the strength and direction
of the linear relationship between two variables, ranging from -1 to +1.
Values near ±1 indicate strong linear relationships, while values near 0
indicate weak or no linear relationship.
2. A correlation coefficient of r = 0.85 indicates:
A) A strong positive linear relationship
B) A weak positive linear relationship
C) A strong negative linear relationship
D) No linear relationship
Correct Answer: A strong positive linear relationship
Rationale: An r value of 0.85 is close to +1, indicating a strong positive linear
relationship between the two variables. As one variable increases, the other
tends to increase as well.
3. A correlation coefficient of r = -0.75 indicates:
,A) A strong positive linear relationship
B) A weak positive linear relationship
C) A strong negative linear relationship
D) No linear relationship
Correct Answer: A strong negative linear relationship
Rationale: An r value of -0.75 is close to -1, indicating a strong negative
linear relationship. As one variable increases, the other tends to decrease.
4. A correlation coefficient of r = 0.12 indicates:
A) A strong positive linear relationship
B) A weak positive linear relationship
C) A strong negative linear relationship
D) No linear relationship
Correct Answer: A weak positive linear relationship
Rationale: An r value of 0.12 is close to 0, indicating a weak positive linear
relationship. There is little to no linear association between the variables.
5. The coefficient of determination r² measures:
A) The slope of the regression line
B) The strength and direction of the linear relationship
C) The proportion of the variance in y that is explained by the linear
relationship with x
D) The predicted value of y
, Correct Answer: The proportion of the variance in y that is explained by the
linear relationship with x
Rationale: r² represents the proportion of the variance in the response
variable y that is explained by the linear relationship with the predictor
variable x. It is always between 0 and 1.
6. If r² = 0.64, what is the correlation coefficient r?
A) 0.64
B) 0.80
C) 0.32
D) 0.40
Correct Answer: 0.80
Rationale: r² = 0.64, so r = √0.64 = 0.80. The correlation coefficient is the
positive square root of r² (assuming a positive relationship).
7. If r² = 0.36, what is the correlation coefficient r?
A) 0.36
B) 0.60
C) 0.18
D) 0.72
Correct Answer: 0.60
Rationale: r² = 0.36, so r = √0.36 = 0.60. This means 36% of the variance in
y is explained by the linear relationship with x.
Learning | 100% PASS
1. The correlation coefficient r measures:
A) The slope of the regression line
B) The strength and direction of the linear relationship between two variables
C) The proportion of variance explained
D) The predicted value of y
Correct Answer: The strength and direction of the linear relationship between
two variables
Rationale: The correlation coefficient r measures the strength and direction
of the linear relationship between two variables, ranging from -1 to +1.
Values near ±1 indicate strong linear relationships, while values near 0
indicate weak or no linear relationship.
2. A correlation coefficient of r = 0.85 indicates:
A) A strong positive linear relationship
B) A weak positive linear relationship
C) A strong negative linear relationship
D) No linear relationship
Correct Answer: A strong positive linear relationship
Rationale: An r value of 0.85 is close to +1, indicating a strong positive linear
relationship between the two variables. As one variable increases, the other
tends to increase as well.
3. A correlation coefficient of r = -0.75 indicates:
,A) A strong positive linear relationship
B) A weak positive linear relationship
C) A strong negative linear relationship
D) No linear relationship
Correct Answer: A strong negative linear relationship
Rationale: An r value of -0.75 is close to -1, indicating a strong negative
linear relationship. As one variable increases, the other tends to decrease.
4. A correlation coefficient of r = 0.12 indicates:
A) A strong positive linear relationship
B) A weak positive linear relationship
C) A strong negative linear relationship
D) No linear relationship
Correct Answer: A weak positive linear relationship
Rationale: An r value of 0.12 is close to 0, indicating a weak positive linear
relationship. There is little to no linear association between the variables.
5. The coefficient of determination r² measures:
A) The slope of the regression line
B) The strength and direction of the linear relationship
C) The proportion of the variance in y that is explained by the linear
relationship with x
D) The predicted value of y
, Correct Answer: The proportion of the variance in y that is explained by the
linear relationship with x
Rationale: r² represents the proportion of the variance in the response
variable y that is explained by the linear relationship with the predictor
variable x. It is always between 0 and 1.
6. If r² = 0.64, what is the correlation coefficient r?
A) 0.64
B) 0.80
C) 0.32
D) 0.40
Correct Answer: 0.80
Rationale: r² = 0.64, so r = √0.64 = 0.80. The correlation coefficient is the
positive square root of r² (assuming a positive relationship).
7. If r² = 0.36, what is the correlation coefficient r?
A) 0.36
B) 0.60
C) 0.18
D) 0.72
Correct Answer: 0.60
Rationale: r² = 0.36, so r = √0.36 = 0.60. This means 36% of the variance in
y is explained by the linear relationship with x.
