Regression and Correlation: Master Scatter Plots, Correlation Coefficients, and Regression Lines

Question 1

Which of the following equations represents a regression line?

Accepted Answer

y = mx + c

Answer

y = c + mx

Answer

x = my + c

Answer

x = c + my

Question 2

Which scatter plot shows a moderate positive correlation between variables x and y?

Accepted Answer

Answer

Answer

Answer

Question 3

Which scatter plot shows a negative correlation between the two variables?

Accepted Answer

C: Points clustered around a downward diagonal line

Answer

A: Points concentrated along an upward diagonal line

Answer

B: Points randomly scattered across the graph

Answer

D: Points mainly concentrated in the graph's center

Question 4

A regression line has a slope of 2. What does this mean?

Accepted Answer

For every 1 unit increase in x, y increases by 2 units.

Answer

For every 2 unit increase in x, y increases by 1 unit.

Question 5

Which of the following is NOT an assumption of linear regression?

Accepted Answer

The data points fit perfectly on the line of best fit.

Answer

The data points are randomly distributed around the line of best fit.

Question 6

A company wants to predict sales based on advertising expenditure. Which type of regression analysis should they use?

Accepted Answer

Simple linear regression

Answer

Multiple linear regression

Question 7

Which of the following is the formula for calculating the correlation coefficient?

Accepted Answer

r = (Σ(x - x̄)(y - ȳ)) / √(Σ(x - x̄)²Σ(y - ȳ)²)

Answer

r = (Σ(x - y)) / √(Σ(x - x̄)²Σ(y - ȳ)²)

Answer

r = (Σ(x + y)) / √(Σ(x - x̄)²Σ(y - ȳ)²)

Answer

r = (Σ(x)²Σ(y)²) / √(Σ(x - x̄)²)

Question 8

What does a correlation coefficient of -0.8 indicate?

Accepted Answer

A strong negative correlation

Answer

A strong positive correlation

Answer

A weak positive correlation

Answer

A weak negative correlation

Question 9

Which of the following is NOT a characteristic of a regression line?

Accepted Answer

It always passes through the origin

Answer

It shows the direction and strength of the relationship between two variables

Answer

It is a straight line that best fits the data points

Answer

It can be used to make predictions

Question 10

Which of the following is a limitation of using correlation to make predictions?

Accepted Answer

Correlation does not imply causation

Answer

Correlation coefficients can only take values between -1 and 1

Answer

Predictions made using correlation are always accurate

Answer

Correlation is not affected by outliers

Question 11

What is the purpose of a residual plot?

Accepted Answer

To identify outliers

Answer

To check the linearity of the relationship between two variables

Answer

To calculate the correlation coefficient

Answer

To predict future values

Question 12

Which of the following measures the variance of the residuals?

Accepted Answer

Standard deviation

Answer

Mean absolute deviation

Answer

Correlation coefficient

Answer

Coefficient of determination

Question 13

Which of the following is NOT a measure of the strength and direction of a linear relationship between two variables?

Accepted Answer

Y-intercept of the regression line

Answer

Correlation coefficient

Answer

Coefficient of determination

Answer

Slope of the regression line

Question 14

A scatter plot suggests a positive linear relationship between the independent variable (x) and the dependent variable (y). Based on this observation, we can deduce that:

Accepted Answer

As x increases, y increases.

Answer

As x decreases, y increases.

Answer

As x increases, y stays constant.

Answer

As x increases, y decreases.

Question 15

A scatter plot analysis yields a correlation coefficient of 0. Which of the following is the most accurate conclusion that can be drawn from this result?

Accepted Answer

There is no relationship between the variables.

Answer

There is a strong positive relationship between the variables.

Answer

There is a weak negative relationship between the variables.

Answer

There is an inverse relationship between the variables.

Question 16

Which measure provides the best indication of how much of the variation in the dependent variable (y) can be explained by the independent variable (x)?

Accepted Answer

Coefficient of determination

Answer

Correlation coefficient

Answer

Slope of the regression line

Answer

Y-intercept of the regression line

Question 17

Given a regression line with a slope of 2 and a y-intercept of 5, what is the predicted value of y when x = 3?

Accepted Answer

11

Answer

1

Answer

3

Answer

15

Question 18

A scatter plot reveals a negative linear relationship between the number of hours spent studying and the score achieved on a test. This suggests that:

Accepted Answer

Students who study more hours tend to perform worse on the test.

Answer

Students who study more hours tend to perform better on the test.

Answer

There is no relationship between study time and test performance.

Answer

Students who perform better on the test tend to study more hours.

Question 19

Which of the following describes a positive correlation?

Accepted Answer

As one variable increases in value, the other variable also increases in value.

Answer

As one variable increases in value, the other variable decreases in value.

Answer

There is no clear relationship between the two variables.

Answer

The correlation coefficient between the two variables is negative.

Question 20

Which of the following values represents a strong positive correlation?

Accepted Answer

0.9

Answer

-0.9

Answer

-0.5

Answer

0.5

Question 21

What is a scatter plot primarily used for?

Accepted Answer

Visualizing the relationship between two variables.

Answer

Determining the equation of a regression line.

Answer

Calculating the correlation coefficient.

Answer

Identifying outliers.

Question 22

What does a negative slope of a regression line indicate?

Accepted Answer

As the x-variable increases in value, the y-variable decreases in value.

Answer

As the x-variable increases in value, the y-variable increases in value.

Answer

There is no linear relationship between the variables.

Answer

The relationship between the variables is non-linear.

Question 23

Which of the following scatter plots indicates a positive correlation?

Accepted Answer

An upward sloping scatter plot

Answer

A downward sloping scatter plot

Answer

A scatter plot with no clear pattern

Answer

A curved scatter plot

Question 24

What is the permissible range of values for the correlation coefficient?

Accepted Answer

-1 to 1

Answer

0 to 1

Answer

0 to 10

Answer

-10 to 10

Question 25

What is the primary purpose of a prediction interval?

Accepted Answer

To estimate a new data point's value within a specified confidence range

Answer

To verify the statistical significance of the correlation coefficient

Answer

To ascertain the regression line's slope

Answer

To compute the correlation coefficient

Question 26

Determine the equation of the regression line with a slope of 2 and a y-intercept of -3.

Accepted Answer

y = 2x - 3

Answer

y = 2x + 3

Answer

y = -2x + 3

Answer

y = -2x - 3

Question 27

Which scatter plot exhibits a strong negative correlation?

Accepted Answer

A scatter plot with a downward sloping line and a correlation coefficient of -0.9

Answer

A scatter plot with an upward sloping line and a correlation coefficient of 0.7

Answer

A scatter plot with no apparent pattern and a correlation coefficient of 0.2

Answer

A scatter plot with a curved line and a correlation coefficient of -0.5

Question 28

Explain the difference between correlation and causation.

Accepted Answer

Causation implies correlation, while correlation does not imply causation

Answer

Correlation implies causation, while causation does not imply correlation

Answer

Correlation and causation are synonymous

Answer

There is no distinction between correlation and causation

Question 29

Which of the following is NOT an advantage of regression analysis?

Accepted Answer

Ease of interpretation

Answer

Predicting future values

Answer

Identifying trends in data

Answer

Hypothesis testing

Question 30

What is the purpose of creating a residual plot?

Accepted Answer

To evaluate the assumptions of the regression model

Answer

To predict future values

Answer

To determine the slope of the regression line

Answer

To compute the correlation coefficient

Question 31

Which of the following scatter plots represents a positive correlation between the variables x and y?

Accepted Answer

A scatter plot where the points form an upward-sloping line.

Answer

A scatter plot where the points form a downward-sloping line.

Answer

A scatter plot where the points are randomly scattered.

Question 32

What is the range of possible values for the correlation coefficient between two variables?

Accepted Answer

-1 to 1

Answer

-0.5 to 0.5

Answer

0 to 1

Question 33

What does the slope of a regression line represent?

Accepted Answer

The average change in y for a unit change in x.

Answer

The average change in x for a unit change in y.

Answer

The y-intercept of the regression line.

Question 34

What does the y-intercept of a regression line represent?

Accepted Answer

The value of y when x is 0.

Answer

The value of x when y is 0.

Answer

The slope of the regression line.

Question 35

Which of the following is a limitation of using regression analysis?

Accepted Answer

It can only be used to analyze data that has a linear relationship.

Answer

It can only be used to make predictions about the future.

Answer

It can only be used to analyze data that is normally distributed.

Question 36

What is the purpose of a residual in regression analysis?

Accepted Answer

To measure the difference between the actual value of y and the predicted value of y.

Answer

To measure the slope of the regression line.

Answer

To measure the y-intercept of the regression line.

Question 37

Which of the following is a measure of the strength of the linear relationship between two variables?

Accepted Answer

Correlation coefficient

Answer

Regression coefficient

Answer

Residual

Question 38

What is the difference between correlation and causation?

Accepted Answer

Causation implies correlation, but correlation does not imply causation.

Answer

Correlation implies causation, but causation does not imply correlation.

Answer

Correlation and causation are the same thing.

Question 39

Which of the following is an example of a spurious correlation?

Accepted Answer

The number of ice cream sales increases as the number of drownings increases.

Answer

The number of people who own cars increases as the number of people who own houses increases.

Answer

The number of students who study for a test increases as the number of students who pass the test increases.

Question 40

What is the range of possible values that a correlation coefficient can take?

Accepted Answer

[-1, 1]

Answer

[-∞, ∞]

Answer

[0, 1]

Question 41

Which of the following equations represents a regression line?

Accepted Answer

y = mx + c

Answer

y = x + c

Answer

y = mx

Answer

y = c

Question 42

What is the primary purpose of using a regression line?

Accepted Answer

To predict the approximate value of one variable based on the value of another variable

Answer

To determine the significance of a relationship between two variables

Answer

To fully describe the relationship between two variables

Question 43

Within a regression equation, which variable is being predicted?

Accepted Answer

The dependent variable

Answer

The variable with the higher correlation coefficient

Answer

The independent variable

Answer

The variable with the lower correlation coefficient

Question 44

When interpreting a correlation coefficient, what value indicates the absence of a relationship between two variables?

Accepted Answer

0

Answer

-1

Answer

0.5

Answer

1

Question 45

Which of the following is not considered a limitation of regression analysis?

Accepted Answer

The ability to make predictions about future values

Answer

Restriction to only two variables

Answer

Sensitivity to outliers

Answer

Assumption of a linear relationship between variables

Question 46

Explain the key difference between correlation and causation.

Accepted Answer

Correlation establishes a relationship between variables, but does not imply that one variable directly causes the other

Answer

Correlation and causation are essentially the same concept

Question 47

Which approach is most effective in improving the accuracy of a regression line?

Accepted Answer

Enlarging the sample size

Answer

Reducing the sample size

Answer

Altering the type of regression model

Question 48

A scatter plot shows the number of hours spent studying and exam scores for a group of students.  Which correlation coefficient best describes a strong positive correlation?

Accepted Answer

0.85

Answer

0.05

Answer

-0.92

Question 49

The equation of the regression line for predicting exam score (y) from hours studied (x) is y = 5x + 50. What is the predicted exam score for a student who studies for 3 hours?

Accepted Answer

65

Answer

50

Answer

55

Answer

85

Question 50

Which of the following is NOT a characteristic of a line of best fit?

Accepted Answer

It must pass through all data points.

Answer

It minimizes the sum of the squared residuals.

Answer

It can be used to make predictions.

Answer

It represents the general trend of the data.

Question 51

A study found a correlation coefficient of -0.7 between ice cream sales and umbrella sales. What type of correlation does this represent?

Accepted Answer

Strong negative correlation

Answer

Strong positive correlation

Answer

Weak negative correlation

Answer

No correlation

Question 52

Which of these statements about extrapolation is true?

Accepted Answer

Extrapolation involves making predictions outside the range of the data.

Answer

Extrapolation is only used with linear data.

Answer

Extrapolation is always reliable for making predictions.

Question 53

A scatter plot shows a weak positive correlation between two variables. Which of these values is most likely the correlation coefficient?

Accepted Answer

0.3

Answer

0.9

Answer

-0.6

Answer

-0.1

Question 54

What does the term 'residual' refer to in the context of regression analysis?

Accepted Answer

The difference between the observed value and the predicted value

Answer

The y-intercept of the regression line

Answer

The slope of the regression line

Question 55

If two variables have a correlation coefficient of zero, what does this indicate?

Accepted Answer

There is no linear relationship between the variables.

Answer

One variable causes the other variable to change.

Answer

The variables are perfectly correlated.

Question 56

Which of the following is a benefit of using a scatter plot to visualize data?

Accepted Answer

It helps identify patterns and relationships between variables.

Answer

It provides a precise measure of the correlation coefficient.

Answer

It calculates the equation of the regression line.

Question 57

When is it appropriate to use linear regression to model the relationship between two variables?

Accepted Answer

When the scatter plot shows a linear pattern

Answer

When the correlation coefficient is close to zero

Answer

When the data points are spread out evenly