Q: Given the regression equation $$\hat{y} = 80.9 + 3.22x$$, what is the predicted value of $$y$$ when $$x = 30$$?

$$\hat{y} = 80.9 + 3.22 \times 30 = 177.5$$

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 and a vertical y-axis.

Question 2

What does the linear correlation coefficient $$r$$ measure?

Accepted Answer

The strength of the linear association between two variables.

Question 3

If the computed value of $$r is $$close to 0, what does this indicate?

Accepted Answer

There does not appear to be a linear correlation.

Question 4

A researcher finds $$r = 0.813$$ and a P-value of $$0.000$$ for the correlation between shoe print length and height. What is the correct interpretation?

Accepted Answer

There is sufficient evidence to conclude there is a linear correlation between shoe print length and height.

Question 5

Which of the following is the general form of the regression equation?

Accepted Answer

$$\hat{y} = b_0$ + b_1$ x$$

Question 6

Given the regression equation $$\hat{y} = 80.9 + 3.22x$$, what is the predicted value of $$y$$ when $$x = 30$$?

Accepted Answer

$$\hat{y} = 80.9 + 3.22 	imes 30 = 177.5$$

Question 7

Which of the following statements about P-values is correct?

Accepted Answer

A small P-value (such as 0.05 or less) suggests that the sample results are not likely to occur by chance when there is no linear correlation.

Question 8

Suppose a study finds a correlation coefficient $$r = 0.591$$ with a P-value of $$0.294$$ for $$n = 5$$ samples. What is the correct conclusion?

Accepted Answer

There is not sufficient evidence to conclude there is a linear correlation.

Question 9

Which of the following best describes a linear correlation?

Accepted Answer

A correlation where the plotted points of paired data result in a pattern that can be approximated by a straight line.

Question 10

A scatterplot of weight (kg) vs. pulse rate (beats per minute) shows no distinct pattern. What does this suggest?

Accepted Answer

There is no correlation between weight and pulse rate.

Question 11

If the regression equation for predicting height from shoe print length is $$\hat{y} = 80.9 + 3.22x$$, what does the slope $$3.22$$ represent?

Accepted Answer

For each additional cm in shoe print length, the predicted height increases by 3.22 cm.

Question 12

Which of the following values of $$r$$ indicates the strongest linear correlation?

Accepted Answer

$$r = -0.95$$

Question 13

What is the main purpose of the regression line in a scatterplot?

Accepted Answer

To provide the straight line that best fits the scatterplot of the data.

Question 14

Which scenario below would most likely result in a high P-value when testing for linear correlation?

Accepted Answer

The scatterplot shows no distinct pattern.

Question 15

If the regression equation is $$\hat{y} = 80.9 + 3.22x$$, what is the y-intercept and what does it represent?

Accepted Answer

The y-intercept is 80.9, representing the predicted value of $$y$$ when $$x = 0.$$

Scatterplots, Correlation, and Regression: Exploring Relationships in Data

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