Question 1

Which of the following best describes the purpose of a scatter diagram in statistics?

Accepted Answer

To show the relationship between two variables by plotting data points.

Question 2

In a scatter diagram, which variable is typically plotted on the horizontal axis?

Accepted Answer

Explanatory variable (X)

Question 3

Which statement about the linear correlation coefficient $$r is $$correct?

Accepted Answer

If $$|r| = 1$$, the data points lie exactly on a straight line.

Question 4

Which of the following is NOT a property of the linear correlation coefficient $$r$$?

Accepted Answer

$$r$$ implies causation between variables.

Question 5

Given the following pairs of data: $$(x_1$, y_1$) = (105, 295)$$ and $$(x_2$, y_2$) = (99, 258)$$, what is the slope $$m of $$the line connecting these points?

Accepted Answer

$$m = \frac{295 - 258}{105 - 99} = \frac{37}{6} \approx 6.17$$

Question 6

Which formula correctly represents the least-squares regression line?

Accepted Answer

$$y = mx + b$$

Question 7

If the linear correlation coefficient $$r$$ between two variables is $$-0.85$$, what can be concluded?

Accepted Answer

There is a strong negative linear relationship.

Question 8

Which of the following best describes the difference between correlation and causation?

Accepted Answer

Correlation measures association, while causation indicates that one variable directly affects the other.

Question 9

Given $$r = 0.6$$, what is the coefficient of determination $$R^2$$?

Accepted Answer

$$R^2 = 0.36$

Question 10

What does the coefficient of determination $$R^2$$ represent in regression analysis?

Accepted Answer

The proportion of total variation in the response variable explained by the regression line.

Question 11

A researcher finds a strong linear correlation between ice cream sales and drowning incidents. Which of the following is the best interpretation?

Accepted Answer

There is an association, but not necessarily causation.

Question 12

If the residual for a data point is large, what does this indicate about the regression model?

Accepted Answer

The data point is far from the regression line, indicating poor fit.

Question 13

Which formula is used to calculate the slope $$b_1 of $$the least-squares regression line?

Accepted Answer

$$b_1 = r$$ \frac{s_y}{s_x}$$

Question 14

Which formula is used to calculate the y-intercept $$b_0 of $$the least-squares regression line?

Accepted Answer

$$b_0$$ = \bar{y} - $$b_1$$ \bar{x}$$

Question 15

A medical study finds $$R^2 = 0.80$ for the relationship between exercise hours and cholesterol levels. What does this mean?

Accepted Answer

80% of the variation in cholesterol levels is explained by exercise hours.

Question 16

Which of the following is a correct interpretation of a negative slope in a regression line?

Accepted Answer

As the explanatory variable increases, the response variable decreases.

Question 17

In a real-world scenario, which variable would most likely be considered the explanatory variable in a study of hours studied and exam scores?

Accepted Answer

Hours studied

Question 18

Which of the following best describes a residual in regression analysis?

Accepted Answer

The difference between the observed value and the predicted value.

Question 19

A scientist uses a least-squares regression line to predict plant growth based on sunlight hours. If the regression equation is $$y = 2x + 5$$, what is the predicted plant growth for 8 hours of sunlight?

Accepted Answer

$$y = 2 	imes 8 + 5 = 21$$

Question 20

Which of the following is NOT a valid use of a contingency table?

Accepted Answer

Calculating the linear correlation coefficient.

Describing the Relationship Between Two Variables: Scatter Diagrams, Correlation, and Regression

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