Question 1

Which of the following best describes the relationship shown in a scatter diagram where the points form a straight line sloping upwards from left to right?

Accepted Answer

A strong positive linear relationship

Question 2

Given the regression equation $$\hat{y} = 5.5273 + 0.0116x$$, what does the slope represent in the context of drilling depth and time to drill five feet?

Accepted Answer

For each additional foot of depth, the time to drill five feet increases by 0.0116 minutes, on average.

Question 3

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

Accepted Answer

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

Question 4

If the correlation coefficient $$r$$ for a data set is close to $$0$$, what does this indicate?

Accepted Answer

There is no linear relationship between the variables.

Question 5

Suppose the correlation between ice cream sales and crime rates is high. Which of the following best explains why this does NOT imply causation?

Accepted Answer

There may be a lurking variable, such as temperature, affecting both variables.

Question 6

Given the following data: $$x = [0, 2, 3, 5, 6, 6]$$, $$y = [5.8, 5.7, 5.2, 2.8, 1.9, 2.2]$$, and using the points $$(2, 5.7)$$ and $$(6, 1.9)$$, what is the equation of the line passing through these points?

Accepted Answer

$$y = -0.95x + 7.6$$

Question 7

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

Accepted Answer

It is resistant to outliers.

Question 8

What is the coefficient of determination $$R^2 if $$the correlation coefficient $$r = 0.773$$?

Accepted Answer

$$R^2 = 0.597$

Question 9

In the context of regression, what does the sum of squared residuals represent?

Accepted Answer

The total variation in the response variable not explained by the regression line.

Question 10

Which scenario best illustrates Simpson’s Paradox?

Accepted Answer

A trend observed in several groups reverses when the groups are combined due to a lurking variable.

Question 11

A contingency table is used to:

Accepted Answer

Relate two categorical variables and analyze their association.

Question 12

If the least-squares regression line is used to make predictions for values of the explanatory variable far outside the observed range, this is called:

Accepted Answer

Extrapolation, which is not recommended.

Question 13

Which formula correctly gives the slope $$b_1 of $$the least-squares regression line?

Accepted Answer

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

Question 14

Which of the following best describes a marginal distribution in a contingency table?

Accepted Answer

The frequency or relative frequency distribution of either the row or column variable.

Question 15

If a scatter diagram shows a U-shaped pattern, what can you conclude about the correlation coefficient?

Accepted Answer

The correlation coefficient will be close to $$0.$$

Chapter 4 STATS

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