Question 1

A variable such that its impact on the results cannot be separated from the impact of the explanatory variable on the outcome is called a

Accepted Answer

A confounding variable is a variable that affects the outcome being studied, but is also related to the explanatory variable being studied, making it difficult to determine which variable is truly causing the observed outcome. Consequently, the impact of the confounding variable cannot be separated from the impact of the explanatory variable, leading to potentially biased results.

Question 2

One uses _________ to predict the value of a response variable for a given value of an explanatory variable.

Accepted Answer

Regression is the statistical method used to predict the value of a response variable based on one or more explanatory variables.

Question 3

A study of 6,600 men found that those who consumed a moderate amount of alcohol (one drink or less per night) have lower mortality (on the average) than those who drink none. Is this good evidence that drinking a moderate amount causes lower mortality?

Accepted Answer

The study is observational, not an experiment, which means that we cannot establish a cause-and-effect relationship between moderate alcohol intake and lower mortality. There may be other factors that differentiate moderate drinkers from non-drinkers that are driving the observed association. Therefore, we cannot conclude that drinking a moderate amount causes lower mortality.

Question 4

A random sample of patients who attended a clinic was selected. The age of the patient (years) and the number of days since the last visit were collected and are displayed in the figure below. The least-squares regression line for predicting number of days since the last visit from the age of the patient is y = 600.081 - 8.694x.  The slope of this line is

Accepted Answer

The slope of the least-squares regression line represents the rate of change of the response variable (in this case, number of days since last visit) per unit increase in the predictor variable (in this case, age). Therefore, the slope is -8.694, indicating that for each additional year of age, the predicted number of days since the last visit decreases by approximately 8.694 days.

Question 5

The correlation between two variables x and y is 0.5. If we used a regression line to predict y using x, what percent of the variation in y would be explained?

Accepted Answer

The coefficient of determination, which explains the percentage of variation in y explained by x, is the square of the correlation coefficient. So, 0.5^2 = 0.25 or 25%.

Question 6

Consider a large number of countries around the world. There is a positive correlation between the number of cell phones per person x and the average life expectancy y. Does this mean that we could increase the life expectancy in Rwanda by shipping cell phones to that country?

Accepted Answer

The positive correlation between the number of cell phones per person and life expectancy does not necessarily imply a causal relationship between the two variables. It may be the case that richer countries have both more cell phones per person and higher life expectancies due to various other factors such as better healthcare, education, and infrastructure. Therefore, simply shipping cell phones to a country like Rwanda may not necessarily increase life expectancy without addressing the underlying factors that contribute to the country's lower life expectancy.

Question 7

A social scientist wants to use subjects' number of hours of television watched to predict their score on a test of propensity to violence. Subjects who watch more television do tend to get higher scores on the test. But regressing their violence test score on their hours of television watch explained only 16 percent of the total score. What is the correlation between their hours of television watched and violence test scores?

Accepted Answer

The question is asking for the correlation between hours of television watched and violence test scores. The fact that regressing violence test scores on hours of television watch explains only 16 percent of the total score indicates a weak relationship, but not necessarily a negative one. Therefore, we can rule out answer choices B and D, which suggest a negative correlation. The answer must be a positive correlation, as mentioned in the question stem. Since 16 percent of the variance is explained by the regression, the correlation coefficient (r) can be calculated by taking the square root of 16 percent, which equals 0.4. Therefore, the correct answer is C) 0.40.

Question 8

A least-squares regression line is not just any line drawn through the points of a scatterplot. What is special about a least-squares regression line?

Accepted Answer

A least-squares regression line is the line that minimizes the sum of the squared vertical distances of the data points from the line. This means that the distance between each data point and the line is minimized, ensuring that the line is as close as possible to all of the data points. This is what makes it special compared to other lines drawn through a scatterplot.

Question 9

Perfect correlation means all of the following except

Accepted Answer

Perfect correlation only implies a strong linear relationship between variables, but it does not necessarily imply a causal relationship between them.

Question 10

Suppose that the least-squares regression line for predicting y from x is y = 100 + 1.3x. Which of the following is a possible value for the correlation between x and y?

Accepted Answer

The correlation coefficient (r) is equal to the slope of the least-squares regression line (b) multiplied by the standard deviation of y (sy) divided by the standard deviation of x (sx). Therefore, r = b(sy/sx) = 1.3(sy/sx). Since the slope is positive, the correlation coefficient must also be positive. Therefore, the only possible value from the given choices is 0.5.

Question 11

In a fisheries researcher's experiment, the correlation between the number of eggs in the nest and the number of viable (surviving) eggs for a sample of nests is r = 0.67.
The correlation r = 0.67 shows that the fact that the nests have different number of eggs explains

Accepted Answer

The coefficient of determination, r², is 0.67² = 0.4489, which means about 45% of the variation in the number of surviving eggs is explained by the number of eggs in the nest.

Question 12

A social scientist learns, upon analyzing her data, that the correlation between a subject's hours of television watched and their score on a test that measures propensity to violence is r = 0.3. One way to use r is to compute the percent of the variation in the violence test score that can be explained by the straight-line relationship between that violence test score and hours of television watched. This percent is about

Accepted Answer

The square of the correlation coefficient (r²) represents the proportion of variability in the violence test score that can be explained by the relationship with hours of television watched. In this case, r² = 0.3² = 0.09, which means that only 9% of the variation in the violence test score can be explained by the hours of television watched.

Question 13

A random sample of patients who attended a clinic was selected. The age of the patient (years) and the number of days since the last visit were collected and are displayed in the figure below. The least-squares regression line for predicting number of days since the last visit from the age of the patient is y = 600.081 - 8.694x.  Using this line, you predict that the number of days since last visit to the clinic for a 50-year-old patient will be about

Accepted Answer

The answer of A random sample of patients who attended...

Question 14

If the least-squares regression line for predicting y from x is y = 500 - 20x, what is the predicted value of y when x = 10?

Accepted Answer

When x = 10, substituting into the equation y = 500 - 20x gives y = 500 - 20(10) = 500 - 200 = 300.

Question 15

What can we say about the relationship between a correlation r and the slope b of the least-squares line for the same set of data?

Accepted Answer

The slope and the correlation measure two different things. The slope measures the change in the response variable for a one-unit increase in the explanatory variable, while the correlation measures the strength and direction of the linear relationship between the two variables. The sign of the slope and the correlation cannot be always the same because the slope can be positive or negative, while the correlation can only be positive or negative. However, the sign will be always the same for a positive correlation and a positive slope or for a negative correlation and a negative slope.

Question 16

A high correlation between two variables does not always mean that changes in one cause changes in the other. The best way to get good evidence that cause-and-effect is present is to

Accepted Answer

The best way to establish causality is through a randomized comparative experiment where one variable is manipulated and the other is observed for any changes. This helps to control for other factors that may be influencing the relationship between the two variables. Simply observing a strong correlation or association between two variables does not provide sufficient evidence for causality.

Question 17

A report in a medical journal notes that the risk of developing Alzheimer's disease among subjects who (voluntarily) regularly took the anti-inflammatory drug ibuprofen (the active ingredient in Advil) was about half the risk among those who did not. Is this good evidence that ibuprofen is effective in preventing Alzheimer's disease?

Accepted Answer

The study described is an observational study, meaning that the subjects were not randomly assigned to take ibuprofen or not. There may be other factors (confounding variables) that could have influenced the results, such as overall health or other lifestyle factors. Therefore, a clinical trial would be needed to confirm whether ibuprofen is truly effective in preventing Alzheimer's disease.

Question 18

If there were something genetic which made people simultaneously more susceptible to both smoking and lung cancer, that would be an instance of

Accepted Answer

This situation describes a common response, where a genetic factor leads to both an increased likelihood of smoking and an increased likelihood of developing lung cancer. This is not an example of causation, as one factor (genetics) is not directly causing the other (smoking or lung cancer). It is also not an example of the placebo effect, as that refers to an improvement in symptoms due to a belief in a treatment, not a genetic factor. Confounding refers to a situation where a third variable affects the relationship between two other variables, which is not the case here.

Question 19

A random sample of patients who attended a clinic was selected. The age of the patient (years) and the number of days since the last visit were collected and are displayed in the figure below. The least-squares regression line for predicting number of days since the last visit from the age of the patient is y = 600.081 - 8.694x.  The slope of this line tells us the

Accepted Answer

The slope of the least-squares regression line represents the average change in the dependent variable (number of days since last visit) for every one-unit increase in the independent variable (age of patient), holding all other variables constant. In this case, the slope is -8.694, indicating that for every one year increase in patient age, there is an average decrease of 8.694 days since their last visit. Therefore, choice B is the correct answer.

Question 20

In a fisheries researcher's experiment, the correlation between the number of eggs in the nest and the number of viable (surviving) eggs for a sample of nests is r = 0.67.
The equation of the regression line for number of viable eggs y versus number of eggs in the nest x is y = 0.72x + 17.07. For a nest with 140 eggs, what is the predicted number of viable eggs?

Accepted Answer

The predicted number of viable eggs is calculated by substituting x = 140 into the regression equation: y = 0.72(140) + 17.07 = 118.47, which rounds to 118 eggs.

Quiz 15: Describing Relationships: Regression, Prediction, and Causation