AP Statistics Chapter 3 Review

Questions and Answers

What does a scatterplot show the relationship between?

two quantitative variables

Which variable ALWAYS appears on the horizontal axis of a scatter plot?

the explanatory variable

What words describe direction in a scatterplot?

positive/negative

What words describe outliers/clusters in a scatterplot?

points that are outside most data Signup and view all the answers

What words describe form in a scatterplot?

linear and non-linear Signup and view all the answers

What words describe strength in a scatterplot?

very strong, moderately strong, fairly weak Signup and view all the answers

What does the correlation measure?

the strength of a linear relationship Signup and view all the answers

Two variables must both be quantitative in order to find the correlation between them.

True Signup and view all the answers

What does an R value of 1 indicate?

positive correlation and perfect association Signup and view all the answers

Is correlation resistant to extreme observations? Explain.

No, it affects correlation significantly Signup and view all the answers

What is the general form of a regression equation? Define each variable.

y(hat) = a + bx; y(hat) = predicted y value, b = predicted slope, and a = predicted y-intercept Signup and view all the answers

What is the difference between y and y hat?

y = actual responsive value, y hat = predicted responsive value Signup and view all the answers

What is extrapolation and why is it dangerous?

making predictions for explanatory variables outside the range of observed data; it can be very inaccurate Signup and view all the answers

What does an R value of 0.45 indicate?

positive, fairly weak association Signup and view all the answers

If a least squares regression line fits the data well, what characteristic should the residual plot exhibit?

no leftover pattern Signup and view all the answers

What does an R value of 0.9 indicate?

positive and very strong association Signup and view all the answers

When reporting a regression, should r or r2 be used to describe the success of the regression? Explain.

r2 and r; r describes correlation Signup and view all the answers

What does an R value of 0 indicate?

no direction and no association Signup and view all the answers

What is the difference between an outlier and an influential point? Is an influential point necessarily an outlier?

No; an outlier is an extreme point off of all data, while an influential point is an extreme point on the overall path of data Signup and view all the answers

What does an R value of -0.3 indicate?

negative and fairly weak association Signup and view all the answers

Why does association not imply causation?

just because two variables correlate mathematically does not mean that they influence each other Signup and view all the answers

What does an R value of -0.8 indicate?

negative and very strong association Signup and view all the answers

What is the standard deviation of the residuals? Provide the symbol and how to interpret it.

symbol: s; interpretation: 'the prediction error between actual (y-value) and predicted (y-value) is...' Signup and view all the answers

What does an R value of -1 indicate?

negative and perfect association Signup and view all the answers

What is the coefficient of determination? Provide the symbol and how to interpret it.

symbol: r2; interpretation: '( )% of the variation in (RV) is accounted for in the linear model.' Signup and view all the answers

What is the correlation coefficient? Provide the symbol and formula.

symbol: r; formula: square root of r2; interpretation: 'Ex: strong, positive association' Signup and view all the answers

What is the slope of a regression equation? Provide the symbol, formula, and how to interpret it.

symbol: b; formula: r times sy over sx; interpretation: 'The RV is predicted to change by ( ) for every one unit change in the EV.' Signup and view all the answers

What is the Y-Intercept of a regression equation? Provide the symbol, formula, and how to interpret it.

symbol: a; formula: y(hat) - bx; interpretation: 'The value of (RV) is predicted to be ( ) when (EV) is 0.' Signup and view all the answers

What are residuals? Provide the symbol, formula, and how to interpret it.

symbol: res; formula: y - y(hat); interpretation: 'Difference between actual y-value and predicted y-value.' Signup and view all the answers

Study Notes

Scatterplots and Variables

Scatterplots visualize the relationship between two quantitative variables.
The explanatory variable is always represented on the horizontal axis of a scatterplot.

Describing Relationships

Direction can be classified as positive or negative.
Outliers are points that lie outside the general pattern of data; clusters group points close together.
Forms of relationships can either be linear or non-linear.
Strength of a relationship is characterized by terms such as very strong, moderately strong, or fairly weak.

Correlation

Correlation measures the strength of a linear relationship between two variables.
Both variables must be quantitative to determine correlation.
An R value of 1 indicates a perfect positive correlation; an R value of 0 indicates no correlation.
Correlation is affected by extreme observations and is not resistant to outliers.

Regression Analysis

The general form of a regression equation is y(hat) = a + bx, where:
- y(hat) is the predicted y value,
- b is the slope,
- a is the y-intercept.
The distinction between actual and predicted values is defined as y (actual value) vs. y(hat) (predicted value).
Extrapolation refers to predictions made outside the range of observed data, which can lead to inaccuracies.

Residual Analysis

For a well-fitted least squares regression line, the residual plot should show no discernible pattern.
Residuals represent the difference between actual y-values and predicted y-values and are calculated by y - y(hat).

Associations and Causation

Associations do not imply causation; correlation between variables does not confirm that they influence each other.

Coefficient and Interpretation

The coefficient of determination (r²) reflects the percentage of variation in the response variable accounted for by the model.
The correlation coefficient (r) indicates the strength and direction of a linear relationship and is derived from the square root of r².
The slope (b) of the regression equation indicates how much the response variable (RV) is expected to change with each unit change in the explanatory variable (EV).
The y-intercept (a) predicts the value of the RV when the EV is zero.

Value Associations

R values indicate the strength and direction of associations:
- R = 0.45 suggests a positive, fairly weak association.
- R = 0.9 suggests a positive, very strong association.
- R = -0.3 indicates a negative, fairly weak association.
- R = -0.8 indicates a negative, very strong association.
- R = -1 indicates a negative, perfect association.

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Test your understanding of scatterplots and relationships between quantitative variables with these flashcards. This quiz covers key concepts related to explanatory variables and the description of data trends, including outliers and clusters. Perfect for AP Statistics students preparing for exams!