Q: Given the regression equation $$y = 125.4 + 1.73x$$, where $$x is $$shoe print length (cm) and $$y is $$height (cm), what is the predicted height for a shoe print length of $$30 cm$$?

$$y = 125.4 + 1.73 \times 30 = 177.3 cm$$

Question 1

Which of the following best describes a scatterplot?

Accepted Answer

A plot of paired (x, y) quantitative data with a horizontal x-axis for the first variable and a vertical y-axis for the second variable.

Question 2

Suppose you have a scatterplot of students' study hours (x) and their exam scores (y). The points form a pattern that can be approximated by a straight line. What type of correlation is present?

Accepted Answer

Linear correlation

Question 3

The linear correlation coefficient $$r is $$used to measure:

Accepted Answer

The strength of the linear association between two variables.

Question 4

If the computed value of $$r is$$ $$0.95$$, what does this indicate about the relationship between the two variables?

Accepted Answer

There is a strong linear correlation.

Question 5

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

Accepted Answer

$$r is $$always between $$-1$$ and $$1.$$

Question 6

A researcher finds $$r = 0.02$$ for the relationship between shoe size and IQ in a sample of 100 adults. What is the best interpretation?

Accepted Answer

There is no significant linear correlation.

Question 7

Given the regression equation $$y = 125.4 + 1.73x$$, where $$x is $$shoe print length (cm) and $$y is $$height (cm), what is the predicted height for a shoe print length of $$30 cm$$?

Accepted Answer

$$y = 125.4 + 1.73 	imes 30 = 177.3 cm$$

Question 8

Which scenario is most likely to show no correlation on a scatterplot?

Accepted Answer

Weight and pulse rate

Question 9

If the P-value for a correlation test is $$0.000$$, what does this imply?

Accepted Answer

There is sufficient evidence to conclude a significant correlation exists.

Question 10

Which of the following is the correct regression equation format for predicting $$y$$ from $$x$$?

Accepted Answer

$$y = b_0$ + b_1x$$

Question 11

A scatterplot of arm circumference (y) versus waist circumference (x) shows a distinct upward pattern. What does this suggest?

Accepted Answer

There is a positive linear correlation.

Question 12

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

Accepted Answer

$$r$$ can be used to measure nonlinear relationships.

Question 13

If a scatterplot shows no distinct pattern, what is the most likely value of $$r$$?

Accepted Answer

$$r is $$close to $$0$$

Question 14

A medical researcher wants to determine if there is a linear relationship between blood pressure and age. Which statistical tool should they use?

Accepted Answer

Scatterplot and linear correlation coefficient $$r$$

Question 15

Which of the following best describes the regression line?

Accepted Answer

A straight line that best fits the scatterplot of paired data.

Question 16

If the sample size increases, what generally happens to the reliability of the correlation coefficient $$r$$?

Accepted Answer

Reliability increases.

Question 17

A scatterplot of hours spent exercising (x) and cholesterol level (y) shows a downward trend. What does this indicate?

Accepted Answer

A negative linear correlation

Question 18

Which of the following is a plausible reason for a misleading graph?

Accepted Answer

Distorting the scale of axes

Question 19

A regression equation is given by $$y = 50 + 2x. If$$ $$x = 10$$, what is the predicted value of $$y$$?

Accepted Answer

$$y = 70$$

Question 20

Which of the following is the best way to determine if two variables are linearly correlated?

Accepted Answer

Calculate the linear correlation coefficient $$r$$ and examine the scatterplot.

Exploring Data with Tables and Graphs: Scatterplots, Correlation, and Regression

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