Chapter 10 - Relationships between Numeric Variables: Regression and Correlation

Question 1

What to look for in a scatter plot:

Answer 1

Trend (pattern), scatter, outliers, strength of the relationship, association, groupings

Question 2

Association

Answer 2

A pattern that connects two (or more) variables. This pattern would be unlikely to be generated by purely chance. Conversely there is no relationship when learning the value of one variable would tell you nothing new about the likely value of the other.

Question 3

Correlation

Answer 3

The strength and direction of the relationship between two numeric variables.

Question 4

Positive correlation

Answer 4

The values of one variable tend to increase as the values of the other variable increase

Question 5

Negative correlation

Answer 5

The values of one variable tend to decrease as the values of the other variable increase.

Question 6

Correlation coefficient

Answer 6

A number between -1 and 1 calculated so that the number represents the strength and direction of the linear relationship between two numeric variables.

Question 7

A correlation coefficient of 1

Answer 7

Indicates a perfect linear relationship with positive slope.

Question 8

A correlation coefficient of -1

Answer 8

Indicates a perfect linear relationship with negative slope

Question 9

Direction

Answer 9

A descriptor of whether an association between two variables is positive or negative

Question 10

Explanatory variable

Answer 10

A variable that we want to use to try to explain or predict the behaviour of a response variable, or just to investigate whether this might be possible.

Question 11

Extrapolate

Answer 11

To estimate the value of one variable based on knowing the value of the other variable, where the known value is outside the range of values of that variable for the data on which the estimation is based.

Question 12

Least squares regression line

Answer 12

A line used to represent a linear trend between the two numeric variables displayed in a scatter plot where the line is chosen to minimise the sum of the squares of the residuals.

Question 13

(Simple) linear regression

Answer 13

A procedure used when one numeric variable (explanatory) is used to predict or explain the behaviour of a second numeric variable (response variable) and the overall pattern between the two variables can be represented by a line.

Question 14

Linear trend

Answer 14

The overall pattern between the two numeric variables displayed in a scatter plot when that pattern can be represented by a line,

Question 15

Outlier(s)

Answer 15

Value(s) that lie so far away from the bulk of the data that they look odd and make us wonder “is that a mistake?”

Question 16

Prediction intertval

Answer 16

This predicts the Y-value for an individual with a specified value of x.

Question 17

Regression line

Answer 17

A line used to represent a linear trend between the two numeric variables displayed in a scatter plot (Alternative name: fitted line)

Question 18

Residual

Answer 18

The difference between an observed value of the response variable and the value of the response variable predicted from the regression line, i.e., observed value - predicted (fitted) value
(Alternative name: prediction error)

Question 19

Scatter

Answer 19

In a scatter plot, the extent to which the values of the response variable deviate from the trend.

Question 20

Trend

Answer 20

The overall pattern between the two numeric variables displayed in a scatter plot.

Question 21

y-intercept

Answer 21

For a point on a line, the value of Y when X = 0. In regression this is often a meaningless value.