Do You Know These Basic Mathematical and Graphical Technique Flashcards

A scatterplot of regression residuals against the explanatory variable and assesses the fit of a regression line; the sum or the mean of its residuals always equals 0.

The difference between an observed value of the response variable and the value predicted by the regression line.

The most effective way to display a relation between 2 quantitative variables

Form: clusters, gaps
Direction: positive or negative association
Strength: how strong is the association
Influential points: outliers or points that fall outside the overall pattern of the relationship
Example:
Form: There's a cluster from 2-3 and 3-4 on the car weight. There's a gap between 4 and 5.
Direction: negative association
Strength: moderately strong
Influential Points: any point above 5.

A positive association has a correlation above 0, while a negative association has a correlation below 0.

R; measurement between 2 quantitative variables to see the direction and strength of a linear relationship of a scatterplot

. r²; variation in y that's explained by the LSRL of y on x.
Wording: (r²)% of the variation is explained by the LSRL(y-hat=a+bx) with ____ as the explanatory variable x and ____ as the response variable y."

Of y on x: makes the sum of the squares of the vertical distances of points from the line as small as possible.
a=y-intercept
b=slope

^
y=predicted y

B=r(s_y/s_x)

_ _
a=y-bx

1. Correlation makes no distinction between explanatory and response variables.
2. Correlation requires that both variables be quantitative, so that it makes sense to do the arithmetic indicated by the formula for r.
3. Because r uses the standardizes values of the observations, r does nor change when we change the units of measurement of x, y, or both.
4. Positive r indicates positive association between the variables, and negative r indicates negative association.
5. The correlation r is always a number between -1 and 1.
6. Correlation measures the strength of only a linear relationship between two variables.
7. Like the mean and standard deviation, the correlation is not resistant: r is strongly affected by a few outlying observations.

Response variable: measures an outcome of a study; dependent variable Explanatory variable: attempts to explain the observed outcomes; independent variable

A scatterplot of regression residuals against the explanatory variable and assesses the fit of a regression line; the sum or the mean of its residuals always equals 0. Data that shows the relationship between two variables

An extreme point on the x-axis direction that influences the regression line.