Question 1

The best fitting line relating the dependent variable y to the independent variable x, often called the regression or least-squares line, is found by minimizing the sum of the squared differences between the data points and the line itself.

Accepted Answer

This is the definition of the least-squares regression line.

Question 2

If the correlation coefficient  , then all the data points lie exactly on a straight line.

Accepted Answer

A correlation coefficient of 1 indicates a perfect positive correlation, meaning all the data points are perfectly aligned on a straight line.

Question 3

The correlation coefficient r is a number that indicates the direction and the strength of the relationship between the dependent variable y and the independent variable x.

Accepted Answer

The correlation coefficient measures the direction and strength of the relationship between two variables, so it is true that it indicates the direction and strength of the relationship between the dependent variable y and the independent variable x.

Question 4

A perfect straight line sloping upward would produce a covariance value of +1.

Accepted Answer

A perfect straight line sloping upward would produce a covariance value of +1 because both variables would increase together in a positive direction.

Question 5

Given the least squares regression line y = 3.8 - 2x,
A) the relationship between x and y is positive
B) the relationship between x and y is negative
C) there is no linear relationship between x and y
D) as x decreases, so does y
E) as x increases, so does y

Accepted Answer

The negative coefficient of x indicates a negative relationship between x and y. As x increases, y decreases.

Question 6

Given that  = 400,  = 625,  = 350, and n = 10, the correlation coefficient is:
A) 0.70
B) 0.56
C) 0.875
D) 0.156
E) 0.141

Accepted Answer

The answer of Given that  = 400,  =...

Question 7

If the correlation coefficient between the independent variable x and the dependent variable y is 0.87, then the best fitting line would have a slope equal to 0.87.

Accepted Answer

The correlation coefficient measures the strength and direction of the linear relationship between two variables, but it does not determine the slope of the best fitting line. The slope of the best fitting line is determined by the data and calculated using regression analysis. Therefore, the correlation coefficient of 0.87 does not necessarily equal the slope of the best fitting line.

Question 8

Generally speaking, if two quantitative variables are unrelated, the covariance will be a positive or negative number close to zero.

Accepted Answer

When two variables are unrelated, their covariance will be close to zero, but it can be positive or negative depending on the specific values of the variables. However, if the variables are truly independent, their covariance will be exactly zero.

Question 9

The standard deviation is a measure of the linear relationship between two quantitative variables.

Accepted Answer

The standard deviation is a measure of the variability or spread of a single quantitative variable, not the relationship between two variables. The correlation coefficient is a measure of the linear relationship between two quantitative variables.

Question 10

The scatterplot is a graph that is used to graphically represent the relationship between two quantitative variables.

Accepted Answer

The definition of a scatterplot is accurate and true.

Question 11

When constructing a scatterplot, the independent variable (x) is placed on the horizontal axis, and the dependent variable (y) is placed on the vertical axis.

Accepted Answer

This is correct. The independent variable (x) is graphed on the horizontal axis or x-axis, and the dependent variable (y) is graphed on the vertical axis or y-axis, in a scatterplot.

Question 12

A perfect correlation between two variables will always produce a correlation coefficient of +1.0.

Accepted Answer

A perfect correlation between two variables can produce a correlation coefficient of +1.0 for a perfect positive correlation or -1.0 for a perfect negative correlation.

Question 13

A perfect straight line sloping downward would produce a covariance value of -1.

Accepted Answer

A perfect straight line sloping downward would have a negative correlation coefficient of -1, which indicates a perfect negative linear relationship and hence a covariance value of -1.

Question 14

If the correlation coefficient  , then there is no linear relationship whatsoever between the dependent variable y and the independent variable x.

Accepted Answer

When the correlation coefficient is 0, it means there is no linear relationship between the two variables, and the dependent variable y and independent variable x are not related.

Question 15

Generally speaking, if two variables are unrelated (as one increases, the other shows no pattern), the covariance will be:
A) a large positive number
B) a large negative number
C) a positive or negative number close to zero
D) a positive or negative number close to 100
E) none of these

Accepted Answer

When two variables are unrelated, there is no systematic relationship between them. As a result, the covariance will be close to zero, regardless of whether it is positive or negative. A large positive or negative number indicates a strong linear relationship between the variables, which is not the case when they are unrelated. A large number close to 100 implies that the variables are nearly perfectly positively or negatively correlated, which is also not the case when they are unrelated. Therefore, the best choice is C.

Question 16

Which of the following are measures of the linear relationship between two variables?
A) the covariance
B) the correlation coefficient
C) the variance
D) both the covariance and the correlation coefficient
E) both the correlation coefficient and the variance

Accepted Answer

Both the covariance and correlation coefficient are measures of the linear relationship between two variables. Variance is a measure of the spread of data, but not specifically of the relationship between two variables.

Question 17

If two variables have a correlation coefficient equal to 0.005, this means that there is no relationship between the two variables.

Accepted Answer

A correlation coefficient of 0.005 indicates a weak, but not necessarily nonexistent, relationship between the two variables.

Question 18

If the linear relationship between the dependent and independent variables is positive, the scatterplot will show the data points on the (x, y) plane generally moving from the lower left corner to the upper right corner.

Accepted Answer

A positive linear relationship means that as the independent variable increases, the dependent variable also tends to increase. This results in points on the scatterplot generally moving from the lower left corner to the upper right corner.

Question 19

A scatterplot is not particularly useful in determining if the relationship between the independent and dependent variables is not linear.

Accepted Answer

A scatterplot can help visualize the relationship between two variables but it may not always indicate whether the relationship is linear or not. Additional analyses, such as correlation coefficients or regression models, may be necessary to determine the linearity of the relationship.

Question 20

If a regression line has a y-intercept of 6.75 and a slope of 1.25, then when x = 2 the actual value of y is:
A) 9.25
B) 8.75
C) 2.25
D) 1.45
E) unknown

Accepted Answer

The answer of If a regression line has a y-intercept...

Quiz 3: Describing Bivariate Data

The best fitting line relating the dependent variable y to the independent variable x, often called the regression or least-squares line, is found by minimizing the sum of the squared differences between the data points and the line itself.

If the correlation coefficient , then all the data points lie exactly on a straight line.

The correlation coefficient r is a number that indicates the direction and the strength of the relationship between the dependent variable y and the independent variable x.

A perfect straight line sloping upward would produce a covariance value of +1.

Given the least squares regression line y = 3.8 - 2x,

Given that = 400, = 625, = 350, and n = 10, the correlation coefficient is: