Question 1

Scattergrams give information about the ____ of a relationship.

Accepted Answer

Scattergrams give information about the strength, direction, and linearity of a relationship between two variables.

Question 2

On a scattergram,the regression line

Accepted Answer

The regression line is a line that represents the best fit for the data points on a scattergram. It is drawn in such a way that it comes as close as possible to touching every score. Therefore, option C is the correct answer. Option A is incorrect because the regression line is not drawn parallel to the horizontal axis. Option B is incorrect because the regression line is not always perpendicular to the vertical axis. Option D is incorrect because the regression line does not necessarily touch at least half of the scores.

Question 3

If the regression line on a scattergram slopes upward from left to right,the relationship is

Accepted Answer

When the regression line slopes upward from left to right, it indicates a positive relationship between the two variables. Therefore, the correct choice is D, positive.

Question 4

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

Accepted Answer

Pearson's r is appropriate for situations in which both variables are interval-ratio in level of measurement as it measures the strength and direction of linear association between the two variables.

Question 5

By convention,the dependent variable is arrayed along the ____ in a scattergram.

Accepted Answer

Conventionally, the dependent variable is plotted on the vertical axis (the ordinate) and the independent variable on the horizontal axis (the abscissa) in a scattergram.

Question 6

For interval-ratio level variables,the scattergram is analogous to ____ for nominal and ordinal level variables.

Accepted Answer

For interval-ratio level variables, the scattergram shows the relationship between two variables, just like bivariate tables show the relationship between two nominal or ordinal level variables. Therefore, the best choice is D, bivariate tables. Choices A, B, and C are not applicable for interval-ratio level variables.

Question 7

For summarizing the relationship between X and Y,the points of minimized variation for the conditional distributions of Y provide us with

Accepted Answer

The points of minimized variation for the conditional distributions of Y provide us with the best fitting regression line. This line represents the relationship between X and Y that minimizes the sum of the squared deviations between the observed values of Y and the corresponding predicted values of Y from X. Therefore, the best choice is B.

Question 8

In a scattergram,the point of minimized variation for scores of Y for a given value of X (the independent variable)is

Accepted Answer

The point of minimized variation for scores of Y for a given value of X is the mean of the conditional Y scores. This is because the mean represents the central tendency for a set of data, and when we calculate the mean of the conditional Y scores for a specific value of X, we are finding the average value for the data points that fall on that specific point on the X-axis. This will give us an indication of where most of the data points are centered around, and therefore where the point of minimized variation is located.

Question 9

Visual examination of a scattergram indicates the existence of an association between variables when

Accepted Answer

The distribution of Y changing as X changes is indicative of a relationship between the two variables, as one variable is impacting the distribution of the other. This is a key characteristic of an association between variables in a scatterplot. The other answer choices are not indicative of an association between variables.

Question 10

The symbol Y¢ ("Y-prime")stands for

Accepted Answer

Y¢ ("Y-prime") is used to represent the predicted score on Y based on the regression equation. Therefore, choice D is the best option. Choices A, B, and C are incorrect as they do not reflect the meaning of Y¢.

Question 11

The conditional mean of Y for any value of X is found by

Accepted Answer

The conditional mean of Y for any value of X is found by taking all the Y scores corresponding to that specific value of X, adding them up, and then dividing by the number of observations (N) corresponding to that specific value of X. This is the definition of the conditional mean and is represented mathematically as E(Y|X=x) = ΣY/N. Therefore, choice A is the correct answer. The other options are not accurate representations of how to find the conditional mean of Y for any value of X.

Question 12

Scattergrams do NOT give information about the ____ of a relationship.

Accepted Answer

Scattergrams, also known as scatter plots, can show the direction, strength, and linearity of a relationship between two variables. However, they do not provide information on the significance of the relationship, which requires statistical testing.

Question 13

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

Accepted Answer

The line that comes as close as possible to touching every score on a scattergram is called the regression line. This line is used to estimate or predict the value of one variable based on the value of another variable.

Question 14

One key assumption of correlation analysis is that the variables have an essentially ____ relationship.

Accepted Answer

Correlation analysis assumes a linear relationship between the variables. This means that the relationship between the variables can be represented by a straight line, and that the strength and direction of the relationship remains constant throughout the range of values for the variables. Nonlinear, curvilinear, or circular relationships would not be appropriate for correlation analysis.

Question 15

By convention,the independent variable is arrayed along the ____ in a scattergram.

Accepted Answer

The convention is to place the independent variable (also known as the predictor variable) along the horizontal axis (the abscissa) in a scattergram. This allows for easy comparison of the relationship between the independent and dependent variables (also known as the response variable) as the values of the independent variable change. The dependent variable is then arrayed along the vertical axis (the ordinate).

Question 16

A perfect association between variables can be seen on a scattergram when

Accepted Answer

When all dots lie on the regression line, it indicates a perfect linear relationship between the two variables. This means that as one variable increases, the other variable also increases at a consistent rate. Therefore, the regression line accurately predicts the value of one variable based on the value of the other variable, and vice versa.

Question 17

There is no linear relationship between two interval-ratio variables when the regression line on a scattergram

Accepted Answer

When the regression line is parallel to the horizontal axis, it indicates that there is no relationship between the two variables. This means that changes in the values of one variable do not have a consistent effect on the values of the other variable. Therefore, there is no linear relationship between them.

Question 18

When referring to interval-ratio variables,a commonly used synonym for association is

Accepted Answer

Association refers to the extent to which two variables are related. In the context of interval-ratio variables, this is often measured using correlation coefficients, making option C the best choice. Probability refers to the likelihood of an event occurring, while predictability refers to the extent to which a variable can be accurately predicted from another variable. Causation refers to a direct relationship between two variables, where changes in one variable directly cause changes in another. While causation may be related to association, they are not synonyms.

Question 19

If a line is drawn through the conditional means of Y,the line will

Accepted Answer

Conditional means of Y may not follow a perfectly linear pattern, especially if there is a non-linear relationship between X and Y. Therefore, the line drawn through the conditional means of Y may also deviate from a perfectly straight line.

Question 20

The direction of a relationship between variables can be detected on a scattergram by considering the angle of the regression line.The relationship is

Accepted Answer

A positive relationship means that as one variable increases, the other variable also tends to increase. This is indicated on a scattergram by a regression line that slopes upward from left to right. Therefore, Choice A is correct. Choices B to D are incorrect.

Quiz 15: Association Between Variables Measured at the Interval-Ratio Level