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The Practice of Statistics - Chapter 3
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Terms in this set (18)
Response Variable
measure the outcome of a study.
Explanatory Variable
may help explain or influence changes in a response variable.
scatterplot
shows the relationship between two quantitative variables measured on the same individuals. The values of one variable may appear on the horizontal axis, and the values of the other variable appear on the vertical axis. Each individual in the data appears as a point in the graph.
explanatory variable goes on the x-axis
Interpreting scatterplots
1) the direction
2) the form
3) the strength of the relationship
- look for outliers
Positive Association
when above average values of one tend to accompany above-average values of the other, and when below-average values also tend to occur together.
Negative Association
when above-average values of one tend to accompany below-average values of the other.
correlation r
measures the direction and strength of the linear relationship between two quantitate variables.
Facts about correlation
1. correlation makes no distinction between explanatory and response variable
2. r does't change when we change the units of measurement of x, y, or both.
3. The correlation r itself has no unit of measurement. It is just a number.
4. Correlation requires that both variables be quantitative
5. Correlation doesn't describe curved relationships between variables, no matter how strong the relationship is.
6. Like the mean and SD, the correlation is not resistant: r is strongly affected by a few outlying observations.
7. Correlation is not a complete summary of two-variable data.
Regression line
is a line that describes how a response variable y changes as an explanatory variable x changes. We often use a regression time to predict the value of y given value of x.
Regression line equation
ŷ = a +bx
- ŷ is the
predicted value
* of the response variable y for a given value of the explanatory variable x.
- b is the
slope
- a is the
y-intercept
, the predicted value of y when x=0
Extrapolation
is the use of a regression line for prediction far outside the interval of values of the explanatory variable x used to obtain the line. Often not accurate.
Residual
is the difference between an observed value of the response variable and the value predicted by the regression line.
residual = observed y - predicted value
r = y - ŷ
least-squares regression line
of y on x is the line that makes the sum of the squared residuals as small as possible
Residual plot
is a scatterplot of the residuals against the explanatory variable. Help us assess how well a regression line fits the data.
Standard deviation of the residuals
the value gives the approximate size of a "typical" or "average" prediction error (residual).
Coefficient of determination r^2
is the fraction of the variation in the values of y that is accounted for by the least-sqaures regression line of y on x. We can calculate r^2 using the following formula:
Outlier
is an observation that lies outside the overall pattern of the other observations.
An observation is influential for a stat calculation..
if removing it would markedly change the result of the calculation.
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