Question 1

Which of the following best describes the correlation coefficient $$r$$ between two quantitative variables?

Accepted Answer

It measures the strength and direction of a linear association between two quantitative variables.

Question 2

Suppose you have a scatterplot of Internet penetration (x) and Facebook penetration (y) for 32 countries. If the correlation $$r = 0.614$$, what does this indicate?

Accepted Answer

There is a moderate positive linear association between Internet and Facebook penetration rates.

Question 3

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

Accepted Answer

The value of $$r$$ does not change if the units of measurement for either variable are changed.

Question 4

Given the regression equation $$\y = 61.4 + 2.4x$$\$ for predicting human height (y) from femur length (x), what is the predicted height for a femur length of 50 cm?

Accepted Answer

$$181.4 cm$$

Question 5

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

Accepted Answer

It is resistant to outliers.

Question 6

If a regression line for predicting y from x is given by $$\y = a + bx$$\$$, what does the slope b$ represent?

Accepted Answer

The amount that $$y$$ changes, on average, for a one-unit increase in $$x.$$

Question 7

A country has an Internet penetration rate of 79% and a Facebook penetration rate of 13%. On a scatterplot of Internet (x) vs. Facebook (y) use, this point is an outlier. What does this mean in context?

Accepted Answer

The country has a much lower Facebook use than expected given its high Internet use.

Question 8

Which of the following best describes the $$R^2 ($$squared correlation) statistic in regression analysis?

Accepted Answer

It is the proportion of the variability in the response variable that is explained by the linear relationship with the explanatory variable.

Question 9

Given $$r = 0.614$$ for Internet and Facebook use, what percentage of the variability in Facebook use is explained by Internet use?

Accepted Answer

$$37.7\%$$

Question 10

Which of the following is the correct formula for the correlation coefficient $$r$$?

Accepted Answer

$$r = \frac{1}{n-1} \sum \left( \frac{x - \overline{x}}{s_x} \right) \left( \frac{y - \overline{y}}{s_y} \right)$$

Question 11

If the regression line for predicting $$y$$ from $$x is$$ $$y = a + bx$$, and the correlation $$r is $$negative, what can you say about the slope $$b$$?

Accepted Answer

The slope $$b$$ will be negative.

Question 12

Which of the following is a correct interpretation of a residual in regression analysis?

Accepted Answer

It is the difference between the observed value and the predicted value for a given $$x.$$

Question 13

Why is the method of least squares used to determine the regression line?

Accepted Answer

It minimizes the sum of the squared residuals between observed and predicted values.

Question 14

Which of the following is TRUE about the regression line obtained by the least squares method?

Accepted Answer

It passes through the point $$(\overline{x}, \overline{y}).$$

Question 15

Suppose you are analyzing the relationship between per capita GDP (x) and life expectancy (y) for several countries. Which variable should be the response variable in a regression analysis?

Accepted Answer

Life expectancy, because we are interested in predicting it from GDP.

Question 16

If the $$y-$$intercept of a regression line is not meaningful in the context of the data, what is the most likely reason?

Accepted Answer

There are no observed $$x$$ values near zero, so predicting $$y$$ when $$x = 0 is $$not relevant.

Question 17

Which of the following would most clearly identify potential outliers in a dataset of Internet and Facebook use for multiple countries?

Accepted Answer

A scatterplot of Internet use vs. Facebook use.

Question 18

If the correlation between two variables is $$r = 0$$, which of the following is TRUE?

Accepted Answer

There is no linear association between the two variables.

Question 19

Which of the following best describes the effect of outliers on the correlation coefficient $$r$$?

Accepted Answer

Outliers can greatly increase or decrease the value of $$r$$, making it not resistant to outliers.

(Lecture 7) Association Between Two Quantitative Variables: Correlation and Regression

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