SOPHIA STATISTICS MILESTONE 5 FORMULAS
AND CALCULATION FLASHCARDS 2026
◉ form. Answer: The overall shape of the data points. The form may
be linear or nonlinear, or there may not be any form at all to the
points if they form a "cloud."
◉ direction. Answer: The way one variable responds to an increase
in the other. With a negative association, an increase in one variable
is associated with a decrease in the other, whereas with a positive
association, an increase in one variable is associated with an
increase in the other.
◉ strength. Answer: The closeness of the points to the indicated
form. Points that are strongly linear will all fall on or near a straight
line.
◉ explanatory variable. Answer: The variable whose increase or
decrease we believe helps explain a tendency to increase or decrease
in some other variable.
◉ response variable. Answer: The variable that tends to increase or
decrease due to an increase or decrease in the explanatory variable.
,◉ correlation. Answer: The strength and direction of a linear
association between two quantitative variables.
◉ correlation coefficient. Answer: The numerical value between -1
and +1 that measures the correlation between two quantitative
variables.
◉ positive correlation. Answer: The type of correlation present
when two variables have a correlation coefficient generally greater
than or equal to 0.5.
◉ negative correlation. Answer: The type of correlation present
when two variables have a correlation coefficient generally less than
or equal to -0.5.
◉ Relative Zero Correlation. Answer: The type of correlation present
when two variables have a correlation coefficient generally between
-0.5 and 0.5.
◉ non-linear relationships. Answer: Associations between two
variables that can be modeled better with a curve than a line.
◉ Coefficient of Determination (r^2). Answer: A value that explains
the percent of variation in the response variable that can be
,explained by a linear association with the explanatory variable. It is
the square of the correlation coefficient.
◉ finding r from r squared. Answer: Step 1: Take the square root of
r2. If only r-squared is given, what you have to do is take the square
root to obtain the correlation coefficient, r.
Step 2: Look at the graph to determine sign. You also have to look at
the graph to find the association--either positive or negative--to
determine the sign of the correlation coefficient.
◉ outlier. Answer: Points that deviate substantially from the overall
form of the remainder of the data points.
◉ influential points. Answer: An observation that, if removed,
significantly changes a statistical measure
◉ inappropriate grouping. Answer: Combining together subgroups
that should not be combined, resulting in a weakened, or even
reversed, association.
◉ correlation. Answer: A statistic which measures the strength and
direction of the linear association between two quantitative
variables.
, ◉ Causation/Cause-and-Effect. Answer: A phenomenon whereby an
increase in one variable directly leads to an increase or decrease in
another variable.
◉ causality. Answer: A cause-and-effect relationship between two
variables.
◉ Best-Fit Line/Trend Line/Regression Line. Answer: A line that
closely approximates the response values for given explanatory
values when the form of the scatterplot is linear.
◉ slope. Answer: The rate of change relating the increase or
decrease in y to an increase of 1 in x.
◉ y-intercept. Answer: The value of y when x = 0.
◉ residual. Answer: The difference between the actual value of the
response variable for a particular data point and its predicted value
from the regression line.
◉ residual plot. Answer: A scatter plot that plots Residuals vs.
explanatory variable, as opposed to response variable vs.
explanatory variable. It can be used to assess the fit of a line.
AND CALCULATION FLASHCARDS 2026
◉ form. Answer: The overall shape of the data points. The form may
be linear or nonlinear, or there may not be any form at all to the
points if they form a "cloud."
◉ direction. Answer: The way one variable responds to an increase
in the other. With a negative association, an increase in one variable
is associated with a decrease in the other, whereas with a positive
association, an increase in one variable is associated with an
increase in the other.
◉ strength. Answer: The closeness of the points to the indicated
form. Points that are strongly linear will all fall on or near a straight
line.
◉ explanatory variable. Answer: The variable whose increase or
decrease we believe helps explain a tendency to increase or decrease
in some other variable.
◉ response variable. Answer: The variable that tends to increase or
decrease due to an increase or decrease in the explanatory variable.
,◉ correlation. Answer: The strength and direction of a linear
association between two quantitative variables.
◉ correlation coefficient. Answer: The numerical value between -1
and +1 that measures the correlation between two quantitative
variables.
◉ positive correlation. Answer: The type of correlation present
when two variables have a correlation coefficient generally greater
than or equal to 0.5.
◉ negative correlation. Answer: The type of correlation present
when two variables have a correlation coefficient generally less than
or equal to -0.5.
◉ Relative Zero Correlation. Answer: The type of correlation present
when two variables have a correlation coefficient generally between
-0.5 and 0.5.
◉ non-linear relationships. Answer: Associations between two
variables that can be modeled better with a curve than a line.
◉ Coefficient of Determination (r^2). Answer: A value that explains
the percent of variation in the response variable that can be
,explained by a linear association with the explanatory variable. It is
the square of the correlation coefficient.
◉ finding r from r squared. Answer: Step 1: Take the square root of
r2. If only r-squared is given, what you have to do is take the square
root to obtain the correlation coefficient, r.
Step 2: Look at the graph to determine sign. You also have to look at
the graph to find the association--either positive or negative--to
determine the sign of the correlation coefficient.
◉ outlier. Answer: Points that deviate substantially from the overall
form of the remainder of the data points.
◉ influential points. Answer: An observation that, if removed,
significantly changes a statistical measure
◉ inappropriate grouping. Answer: Combining together subgroups
that should not be combined, resulting in a weakened, or even
reversed, association.
◉ correlation. Answer: A statistic which measures the strength and
direction of the linear association between two quantitative
variables.
, ◉ Causation/Cause-and-Effect. Answer: A phenomenon whereby an
increase in one variable directly leads to an increase or decrease in
another variable.
◉ causality. Answer: A cause-and-effect relationship between two
variables.
◉ Best-Fit Line/Trend Line/Regression Line. Answer: A line that
closely approximates the response values for given explanatory
values when the form of the scatterplot is linear.
◉ slope. Answer: The rate of change relating the increase or
decrease in y to an increase of 1 in x.
◉ y-intercept. Answer: The value of y when x = 0.
◉ residual. Answer: The difference between the actual value of the
response variable for a particular data point and its predicted value
from the regression line.
◉ residual plot. Answer: A scatter plot that plots Residuals vs.
explanatory variable, as opposed to response variable vs.
explanatory variable. It can be used to assess the fit of a line.
