Question 1

Which of the following best describes the purpose of a scatterplot in statistics?

Accepted Answer

To show the relationship between two numerical variables

Question 2

A teacher collects data on students' test scores and the number of minutes they spent studying. The scatterplot of this data shows that as study time increases, test scores also increase. What type of correlation is this?

Accepted Answer

Positive linear correlation

Question 3

Which statement is true regarding correlation and causation?

Accepted Answer

Correlation does not imply causation

Question 4

Given the following data: as the number of pins on a backpack increases, test scores decrease. What is the slope of the trend line and the type of correlation?

Accepted Answer

Slope is negative; negative correlation

Question 5

A scatterplot of cargo weight (x-axis) versus drone flight duration (y-axis) shows that as cargo weight increases, flight duration decreases. Which of the following best describes this relationship?

Accepted Answer

Negative correlation

Question 6

Which formula is used to calculate the linear correlation coefficient $$r$$ for two variables $$x$$ and $$y$$?

Accepted Answer

$$r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2$ \sum (y_i - \bar{y})^2$}}$$

Question 7

If the correlation coefficient $$r$$ between two variables is close to $$-1$$, what does this indicate?

Accepted Answer

A strong negative linear relationship

Question 8

A marketing researcher finds $$r = 0.59$$ between advertising budget and sales revenue. What does this value suggest?

Accepted Answer

There is a moderate positive linear relationship

Question 9

Which of the following statements about the correlation coefficient $$r is $$FALSE?

Accepted Answer

$$r is $$affected by the slope of the best-fit line

Question 10

Suppose a scientist measures the speed of sound at different altitudes and finds $$r = -0.98. $$What does this value indicate about the relationship between altitude and speed of sound?

Accepted Answer

There is a strong negative linear relationship

Question 11

Which of the following is the correct sequence of steps to create a scatterplot on a TI-84 calculator?

Accepted Answer

Enter data in L1 and L2, turn on STATPLOT, set Xlist and Ylist, adjust window, graph

Question 12

A data set has $$r = 0.13. $$Which of the following best describes the correlation?

Accepted Answer

Weak positive correlation

Question 13

Which of the following real-world scenarios is most likely to have a nonlinear correlation?

Accepted Answer

Amount of fertilizer and crop yield (where too much fertilizer reduces yield)

Question 14

If a scatterplot shows points tightly clustered around a straight line with a positive slope, what can you say about the correlation coefficient $$r$$?

Accepted Answer

$$r is $$close to $$1$$

Question 15

A researcher finds that the number of hours slept the night before an exam and the exam score have $$r = 0.02. $$What does this suggest?

Accepted Answer

There is no significant linear relationship

Question 16

Which of the following is a common misconception about correlation?

Accepted Answer

A high correlation means one variable causes the other

Question 17

A data set has $$r = -0.92. $$Which of the following scatterplots best represents this value?

Accepted Answer

Points closely clustered around a line with a negative slope

Question 18

Which of the following best describes a situation where two variables are correlated but not causally related?

Accepted Answer

Ice cream sales and drowning incidents both increase in summer

Question 19

Which calculator function is used to find the linear correlation coefficient on a TI-84?

Accepted Answer

LinReg(ax+b)

Question 20

A data set has $$r = 0. $$What does this indicate about the relationship between the two variables?

Accepted Answer

There is no linear relationship

Scatterplots and Correlation: Describing the Relation Between Two Variables

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