Q: Given the regression equation $$\text{Height} = 80.9 + 3.22 \times \text{Shoe Print Length}$$, what is the predicted height for a shoe print length of $$30 cm$$?

$$\text{Height} = 80.9 + 3.22 \times 30 = 177.5 cm$$

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 and a vertical y-axis.

Question 2

Suppose you have a scatterplot of waist circumference (x) and arm circumference (y) that shows a clear upward trend. What does this indicate?

Accepted Answer

There is a positive linear correlation between waist and arm circumference.

Question 3

Which value of the linear correlation coefficient $$r$$ indicates the strongest negative linear relationship?

Accepted Answer

$$r = -0.95$$

Question 4

If the computed value of $$r is $$close to 0, what does this suggest about the relationship between two variables?

Accepted Answer

There does not appear to be a linear correlation.

Question 5

A researcher uses Excel to calculate the correlation between shoe print length and height and obtains $$r = 0.59$$ with a p-value of $$0.29. $$What is the correct interpretation?

Accepted Answer

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

Question 6

Which of the following is the general form of the regression equation for a line of best fit?

Accepted Answer

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

Question 7

In a regression analysis, the slope $$b_1 of $$the regression line represents:

Accepted Answer

The estimated change in $$y$$ for a one-unit increase in $$x.$$

Question 8

A p-value in a correlation test is interpreted as:

Accepted Answer

The probability of obtaining a correlation as extreme as the observed one, assuming no linear correlation exists.

Question 9

If the p-value for a correlation test is $$0.0001$$, what conclusion should be drawn?

Accepted Answer

There is strong evidence of a linear correlation between the variables.

Question 10

Given the regression equation $$	ext{Height} = 80.9 + 3.22 	imes 	ext{Shoe Print Length}$$, what is the predicted height for a shoe print length of $$30 cm$$?

Accepted Answer

$$	ext{Height} = 80.9 + 3.22 	imes 30 = 177.5 cm$$

Question 11

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

Accepted Answer

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

Question 12

A scatterplot of weight (x) and pulse rate (y) shows no clear pattern. What does this suggest?

Accepted Answer

There is no linear correlation between weight and pulse rate.

Question 13

Which Excel function can be used to calculate the linear correlation coefficient between two variables?

Accepted Answer

CORREL

Question 14

If the regression output in Excel shows a p-value of $$0.294$$ for the slope, what does this mean?

Accepted Answer

There is not sufficient evidence to conclude a linear relationship between the variables.

Question 15

Which of the following is NOT a requirement for using linear regression?

Accepted Answer

Both variables must be categorical.

Question 16

A student claims that a correlation coefficient of $$r = 0$$ means there is no relationship at all between two variables. Is this correct?

Accepted Answer

No, $$r = 0$$ means there is no linear relationship, but there could be a non-linear relationship.

Question 17

Which scenario best illustrates the use of regression analysis in a real-world context?

Accepted Answer

Predicting a person's height based on their shoe print length at a crime scene.

Question 18

If a regression line has the equation $$\hat{y} = 125.4 + 1.73x$$, what does the value $$125.4$$ represent?

Accepted Answer

The estimated value of $$y$$ when $$x = 0 ($$the y-intercept).

Question 19

Which of the following p-values provides the strongest evidence for a linear correlation?

Accepted Answer

$$0.0001$$

Scatterplots, Correlation, and Regression: Exploring Relationships in Data

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