Question 1

After scores of all cases have been located on a scatterplot, a straight line drawn so that it comes as close as possible to touching every score is called the________.
A) regression line.
B) line of approximation.
C) cluster line.
D) scatterplot summary.

Accepted Answer

The straight line drawn to come as close as possible to touching every score on a scatterplot is called the regression line, which is used to estimate the relationship between two variables. The other options, such as "line of approximation", "cluster line", and "scatterplot summary", are not commonly used or recognized terms in statistics.

Question 2

One important function of the least-squares regression equation is that________.
A) we can use it to tell if a relationship is linear.
B) it summarizes all possible scores on the two variables.
C) it makes the scattergram symmetrical.
D) it allows us to predict Y scores for any value of X.

Accepted Answer

The least-squares regression equation allows us to predict Y scores for any value of X. This is one of the most important functions of the equation, as it helps us understand the relationship between the two variables and make predictions based on that relationship. The other options listed are not correct, as the equation does not indicate if a relationship is linear, summarize all possible scores, or make the scattergram symmetrical.

Question 3

If a = 2 and b = 4, what would the value of Y be when X = 1?
A) 4
B) 6
C) 2
D) 1

Accepted Answer

The problem does not provide a specific equation for Y in terms of X, a, and b. However, if we assume a simple linear relationship such as Y = aX + b, then substituting the given values (a = 2, b = 4, X = 1) results in Y = 2(1) + 4 = 6.

Question 4

If the slope (b) is zero, the value of r________.
A) would also be zero.
B) would be 1.00.
C) would be - 1.00.
D) cannot be determined from the information given.

Accepted Answer

When the slope (b) is zero, r will also be zero. This is because the correlation coefficient r measures the linear relationship between two variables, and if there is no slope (i.e., no change in the y-variable with respect to the x-variable), then there is no linear relationship to measure. Therefore, r will be zero in this case.

Question 5

If you wanted to measure the association between the age of people (in years) and the number of arrests for driving while intoxicated, the most appropriate measure of association would be________.
A) gamma.
B) lambda.
C) phi.
D) Pearson's r.

Accepted Answer

Pearson's r is the most appropriate measure of association for this scenario because it is used to determine the strength and direction of a linear relationship between two continuous variables, such as age (in years) and the number of arrests for driving while intoxicated.

Question 6

The explained variation represents________.
A) the conditional distributions of Y.
B) the amount that Y varies.
C) the improvement in our ability to predict Y when taking X into account.
D) the sum of the squares of all scores of Y.

Accepted Answer

The explained variation, also known as the "explained sum of squares," represents the amount of variation in the dependent variable (Y) that is explained by the independent variable(s) (X). It is a measure of the improvement in our ability to predict Y when taking X into account. Therefore, choice C is the correct answer. The other options do not accurately describe the concept of explained variation.

Question 7

In a study of the relationship between geographical mobility (number of times a person has changed residences) and number of friends, Pearson's r is reported as .40. Which of the following would be a correct interpretation?
A) Mobility explains 16% of the variation in number of friends.
B) There is a strong positive relationship between number of friends and mobility.
C) As mobility increases, number of friends decreases.
D) Mobility explains 40% of the variation in number of friends.

Accepted Answer

Pearson's r is a measure of correlation that ranges from -1 to 1. A value of .40 indicates a moderate positive relationship between geographical mobility and number of friends. According to Cohen's guidelines, a correlation coefficient of .40 can be interpreted as a "moderate" effect size. Additionally, Pearson's r squared (r^2) indicates the amount of variance in one variable that can be explained by the other variable. In this case, r^2 = .16, which means that 16% of the variation in number of friends can be explained by geographical mobility. Therefore, D is the correct interpretation. A is incorrect because it misrepresents the amount of variance explained. B is incorrect because the relationship is only moderate, not strong. C is incorrect because the correlation coefficient indicates a positive relationship, not a negative one.

Question 8

When working with interval-ratio data, the optimal strategy for predicting Y while taking X into account would be to________.
A) use the regression line.
B) guess randomly.
C) ignore the slope (b).
D) always predict the Y intercept (a).

Accepted Answer

When working with interval-ratio data, the most effective strategy for predicting Y while taking X into account is to use the regression line. The regression line takes into account both the slope (b) and the Y intercept (a) and provides the most accurate predicted values of Y for a given value of X. Guessing randomly or ignoring the slope (b) or predicting only the Y intercept (a) would not take into account the relationship between X and Y and would provide inaccurate predictions.

Question 9

A researcher wants to measure the strength of the association between income (measured in dollars per year) and education (measured in number of years of formal schooling). Which of the following would be the most appropriate measure of association?
A) The slope (b)
B) Gamma
C) Chi square
D) Pearson's r

Accepted Answer

Pearson's r is the most appropriate measure of association between two quantitative variables, such as income and education. The slope (b) is a measure of the effect of one variable on another in a regression model, but does not measure association directly. Gamma is a measure of association between two ordinal variables. Chi square is a measure of association between two categorical variables.

Question 10

The amount of error in predicting Y that remains after X has been taken into account is________.
A) the unexplained variation of Y.
B) r - 1.00.
C) always zero.
D) r.

Accepted Answer

The amount of error in predicting Y that remains after X has been taken into account is referred to as the unexplained variation of Y. Choice B (r-1.00) and choice D (r) are incorrect because they do not relate to the unexplained variation of Y. Choice C (always zero) is also incorrect because there will always be some error or variation in predicting Y, even when X is taken into account.

Question 11

If a regression line is parallel to the horizontal axis of the scattergram, the slope (b) will be________.
A) 1.00.
B) -1.00.
C) 0.00.
D) 0.45.

Accepted Answer

When the regression line is parallel to the horizontal axis, it means that there is no relationship between the variables being plotted. Therefore, the slope (b) will be 0.00.

Question 12

A study found that parenting classes were closely related to a child's performance in school. Each week of parenting classes taken by a child's parents raised their high school GPA by 0.23 points. With an intercept of 1.68, what could parents who attended 8 weeks of classes expect to see in their child's subsequent GPA?
A) 2.52
B) 3.21
C) 3.52
D) 3.79

Accepted Answer

The equation for the line is GPA = 1.68 + 0.23 * weeks. Plugging in 8 for weeks, we get GPA = 1.68 + 0.23 * 8 = 3.52.

Question 13

If a = 5 and b = 10, what would the value of Y be when X = 100?________.
A) Unknown, more information is needed
B) 1000
C) 1005
D) 5001

Accepted Answer

Since Y = aX + b, substituting a = 5, b = 10, and X = 100 gives Y = 5(100) + 10 = 510. Therefore, the answer is C.

Question 14

In most correlation matrices, the diagonal line has a value of________.
A) 0.
B) 1.
C) 5.
D) it cannot be predicted.

Accepted Answer

The diagonal line in a correlation matrix represents the correlation of a variable with itself, which is always perfect (i.e., 1) as it reflects the correlation of a variable with itself.

Question 15

The appropriate measure of association for situations in which both variables are interval-ratio in level of measurement is________.
A) Pearson's r.
B) gamma.
C) chi square.
D) the slope (b).

Accepted Answer

Pearson's r is the appropriate measure of association for situations in which both variables are interval-ratio in level of measurement.

Question 16

A study of traffic safety shows a correlation of 0.57 between average speed of traffic and number of fatal accidents for a particular stretch of highway. This means that________.
A) drivers should speed up to get through this area as quickly as possible.
B) as speed increases, fatalities decrease.
C) fatalities tend to increase as average speed increases.
D) every 1 mile per hour increase in average speed increases the number of traffic fatalities by .57.

Accepted Answer

A correlation of 0.57 between average speed of traffic and number of fatal accidents indicates a moderate positive correlation, meaning that fatalities tend to increase as the average speed increases. This does not necessarily mean that increasing speed will always lead to more fatalities, but rather that there is a consistent association between higher speeds and a higher number of fatal accidents. Driving slower and more cautiously may help to reduce the number of fatal accidents on this stretch of highway. Choice A is incorrect because speeding up would likely increase the risk of accidents and fatalities. Choice B is incorrect because the correlation indicates the opposite - as speed increases, fatalities tend to increase. Choice D is incorrect because the correlation does not provide information about the specific increase in fatalities for every mile per hour increase in speed.

Question 17

If the slope of a regression line is 1.5, then________.
A) for every unit of change in X, there is a change of 1.5 units in Y.
B) for every unit of change in Y, there is a change of 1.5 in X.
C) the score of each case is 1.5 times higher on Y than on X.
D) Y causes X

Accepted Answer

The slope of a regression line indicates the change in Y for every unit of change in X. So, if the slope is 1.5, then for every unit of change in X, there is a change of 1.5 units in Y.

Question 18

If we calculate an r of .60, the proportion of the variation of Y that is explained by X is________.
A) .36
B) .40
C) .60
D) .64

Accepted Answer

The proportion of the variation of Y that is explained by X in a correlation is found by squaring the correlation coefficient (r), which in this case is .60. So, .60 squared equals .36.

Question 19

When working with interval-ratio data, the optimal strategy for predicting Y while ignoring X will be to use the________.
A) mode of the Y scores for every case.
B) median Y score for every case.
C) mean Y score for every case.
D) lowest Y score for every case.

Accepted Answer

The mean Y score is the best choice for predicting Y while ignoring X when working with interval-ratio data because it takes into account all of the Y scores in the dataset, and is sensitive to any outliers or extreme values. The mode and median are less effective because they do not consider all of the Y scores in the dataset and may be affected by the presence of outliers. The lowest Y score is not a useful predictor because it only provides information about one particular point in the dataset and does not take into account any other factors.

Question 20

By convention, the independent variable is arrayed along the ______________ in a scatterplot.
A) vertical axis (the ordinate)
B) regression line
C) horizontal axis (the abscissa)
D) calibration line

Accepted Answer

By convention, the independent variable (also known as the explanatory variable or predictor variable) is represented on the horizontal axis (the abscissa) in a scatterplot. The dependent variable (also known as the response variable or outcome variable) is represented on the vertical axis (the ordinate). This is the standard convention followed in many fields, including mathematics, statistics, and science.

Quiz 13: Association Between Variables Measured at the Interval Ratio Level

After scores of all cases have been located on a scatterplot, a straight line drawn so that it comes as close as possible to touching every score is called the________.

One important function of the least-squares regression equation is that________.

If a = 2 and b = 4, what would the value of Y be when X = 1?

If the slope (b) is zero, the value of r________.

If you wanted to measure the association between the age of people (in years) and the number of arrests for driving while intoxicated, the most appropriate measure of association would be________.

The explained variation represents________.

In a study of the relationship between geographical mobility (number of times a person has changed residences) and number of friends, Pearson's r is reported as .40. Which of the following would be a correct interpretation?

When working with interval-ratio data, the optimal strategy for predicting Y while taking X into account would be to________.

A researcher wants to measure the strength of the association between income (measured in dollars per year) and education (measured in number of years of formal schooling) . Which of the following would be the most appropriate measure of association?

The amount of error in predicting Y that remains after X has been taken into account is________.

If a regression line is parallel to the horizontal axis of the scattergram, the slope (b) will be________.

If a = 5 and b = 10, what would the value of Y be when X = 100?________.

In most correlation matrices, the diagonal line has a value of________.

The appropriate measure of association for situations in which both variables are interval-ratio in level of measurement is________.

A study of traffic safety shows a correlation of 0.57 between average speed of traffic and number of fatal accidents for a particular stretch of highway. This means that________.

If the slope of a regression line is 1.5, then________.

If we calculate an r of .60, the proportion of the variation of Y that is explained by X is________.

When working with interval-ratio data, the optimal strategy for predicting Y while ignoring X will be to use the________.

By convention, the independent variable is arrayed along the ______________ in a scatterplot.