Question 1

Which of the following best describes the difference between a response variable and an explanatory variable in a statistical study?

Accepted Answer

The response variable is the outcome we measure, while the explanatory variable is the factor that may influence it.

Question 2

In a study examining the relationship between the number of square feet in a house and the assessed value of the house, which is the explanatory variable and which is the response variable?

Accepted Answer

Assessed value is the response variable; number of square feet is the explanatory variable.

Question 3

A contingency table is used to display data for which type of variables?

Accepted Answer

Two categorical variables

Question 4

Given the following conditional proportions for happiness at each income level: Not too happy (0.16), Pretty happy (0.58), Very happy (0.25), what can you infer about the association between happiness and income?

Accepted Answer

There is no association between happiness and income.

Question 5

In the binge drinking by gender table, what is the marginal proportion of binge drinkers in the sample?

Accepted Answer

$$0.437$$

Question 6

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

Accepted Answer

Correlation $$r$$ measures the strength of a linear relationship between two variables.

Question 7

Suppose the regression equation for predicting height from femur length is $$\hat{y} = 61.4 + 2.4x. $$What does the slope of 2.4 mean in this context?

Accepted Answer

For each 1 cm increase in femur length, the predicted height increases by 2.4 cm.

Question 8

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

Accepted Answer

The actual value minus the predicted value.

Question 9

If the correlation $$r$$ between two variables is close to zero, what does this indicate?

Accepted Answer

There is little to no linear association.

Question 10

Which of the following is a risk when using a regression line to predict values outside the observed range of data?

Accepted Answer

Extrapolation, which may lead to unreliable predictions.

Question 11

A lurking variable is best described as:

Accepted Answer

A variable that is not measured but influences the association between the response and explanatory variables.

Question 12

Which of the following scatterplots would most likely have a correlation $$r$$ closest to $$-0.9$$?

Accepted Answer

A scatterplot where the points fall almost perfectly along a downward sloping straight line.

Question 13

Given the regression equation $$\hat{y} = a + bx$$, what does it mean if $$b = 0$$?

Accepted Answer

There is no association between $$x$$ and $$y.$$

Question 14

Which of the following best describes the meaning of $$r^2 (r-$$squared) in regression analysis?

Accepted Answer

$$r^2 is $$the proportion of variation in $$y$$ explained by the linear relationship with $$x.$$

Question 15

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

Accepted Answer

$$r$$ measures the strength of any type of relationship, linear or nonlinear.

Question 16

In the context of used cars, what type of association would you expect between the age of the car and the resale value?

Accepted Answer

Negative association

Question 17

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

Accepted Answer

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

Question 18

If a data point is an outlier and has a high or low $$x$$ value compared to the rest of the data, what effect can it have on the regression analysis?

Accepted Answer

It can be an influential observation, greatly affecting the regression line and correlation.

Introductory Statistics: Association, Correlation, and Regression Study Guidance

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