Chapter 13- Correlation and Regression

Question 1

correlation

Answer 1

a statistical procedure used to describe the strength and direction of the linear relationship between two factors.

Question 2

Linear regression

Answer 2

also called regression, is a statistical procedure used to determine the equation of a regression line to a set of data points and to determine the extent to which the regression equation can be used to predict values of one factor, given known values of a second factor in a population.

Question 3

scatter plot

Answer 3

also called a scatter gram, is a graphical display of discrete data points (x, y) used to summarize the relationship between two variables.

Question 4

Data points

Answer 4

the x- and y-coordinates for each plot in a scatter plot.

Question 5

correlation coefficient (r)

Answer 5

used to measure the strength and direction of the linear relationship, or correlation, between two factors. The value of r ranges from −1.0 to +1.0.

Question 6

positive correlation

Answer 6

(0 < r ≤ +1.0) is a positive value of r that indicates that the values of two factors change in the same direction: As the values of one factor increase, the values of the second factor also increase; as the values of one factor decrease, the values of the second factor also decrease.

Question 7

negative correlation

Answer 7

(–1.0 ≤ r < 0) is a negative value of r that indicates that the values of two factors change in different directions, meaning that as the values of one factor increase, the values of the second factor decrease.

Question 8

regression line

Answer 8

the best-fitting straight line to a set of data points. A best-fitting line is the line that minimizes the distance of all data points that fall from it.

Question 9

Pearson correlation coefficient (r),

Answer 9

also called the Pearson product-moment correlation coefficient, is a measure of the direction and strength of the linear relationship of two factors in which the data for both factors are measured on an interval or ratio scale of measurement.

Question 10

sum of products (SP)

Answer 10

the sum of squares for two factors, X and Y, which are also represented as SSXY. SP is the numerator for the Pearson correlation formula. To compute SP, we multiply the deviation of each X value by the deviation of each Y value.

Question 11

coefficient of determination (r2 or R2)

Answer 11

a formula that is mathematically equivalent to eta-squared and is used to measure the proportion of variance of one factor (Y) that can be explained by known values of a second factor (X).

Question 12

Homoscedasticity

Answer 12

the assumption that there is an equal (“homo”) variance or scatter (“scedasticity”) of data points dispersed along the regression line.

Question 13

Linearity

Answer 13

the assumption that the best way to describe a pattern of data is using a straight line.

Question 14

Reverse causality

Answer 14

a problem that arises when the causality between two factors can be in either direction.

Question 15

confound variable

Answer 15

or third variable, is an unanticipated variable not accounted for in a research study that could be causing or associated with observed changes in one or more measured variables.

Question 16

Restriction of range

Answer 16

a problem that arises when the range of data for one or both correlated factors in a sample is limited or restricted, compared to the range of data in the population from which the sample was selected.

Question 17

Spearman rank-order correlation coefficient (rs)

Answer 17

or Spearman’s rho, is a measure of the direction and strength of the linear relationship of two ranked factors on an ordinal scale of measurement.

Question 18

point-biserial correlation coefficient (rpb)

Answer 18

a measure of the direction and strength of the linear relationship of one factor that is continuous (on an interval or ratio scale of measurement) and a second factor that is dichotomous (on a nominal scale of measurement).

Question 19

phi correlation coefficient (rϕ)

Answer 19

a measure of the direction and strength of the linear relationship of two dichotomous factors on a nominal scale of measurement.

Question 20

slope (b)

Answer 20

The slope (b) of a straight line is used to measure the change in Y relative to the change in X. When X and Y change in the same direction, the slope is positive. When X and Y change in opposite directions, the slope is negative.

Question 21

y-intercept (a)

Answer 21

The y-intercept (a) of a straight line is the value of the criterion variable (Y) when the predictor variable (X) equals 0.

Question 22

method of least squares

Answer 22

a statistical procedure used to compute the slope (b) and y-intercept (a) of the best-fitting straight line to a set of data points.

Question 23

Analysis of regression,

Answer 23

or regression analysis, is a statistical procedure used to test hypotheses for one or more predictor variables to determine whether the regression equation for a sample of data points can be used to predict values of the criterion variable (Y) given values of the predictor variable (X) in the population.

Question 24

Regression variation

Answer 24

the variance in Y that is related to or associated with changes in X. The closer data points fall to the regression line, the larger the value of regression variation.

Question 25

Residual variation

Answer 25

the variance in Y that is not related to changes in X. This is the variance in Y that is left over or remaining. The farther data points fall from the regression line, the larger the value of residual variation.

Question 26

standard error of estimate (se)

Answer 26

an estimate of the standard deviation or distance that a set of data points falls from the regression line. The standard error of estimate equals the square root of the mean square residual.

Question 27

Three key characteristics are illustrated in this exercise: (adding a constant etc)

Answer 27

1. Adding or subtracting a constant to one set of scores (X or Y) does not change the correlation coefficient.
2. Multiplying or dividing one set of scores (X or Y) by a positive constant does not change the correlation coefficient.
3. Multiplying or dividing one set of scores (X or Y) by a negative constant changes only the sign (or direction) of the correlation. The strength of the correlation coefficient remains unchanged.

Question 28

• Univariate Outlier:

Answer 28

An observation that is unusual in either x or y is called a univariate outlier. While interesting, these are not as important in the regression context.

Question 29

• Regression Outliers

Answer 29

Data points that aren’t very well predicted by the model (deviate from the regression line) and have a large residual. Regression outliers can decrease model fit (e.g. r2) and affect parameter estimates (slope and intercept).

Question 30

• Influence:

Answer 30

When a data point is extreme on x and an outlier on y, it can greatly affect the model parameter estimates compared to if it weren’t in the sample. It is considered an influential case.