Ch. 7: Scatterplots, Association, and Correlation

1. Know the definition & properties of correlation (correlation coefficient)
  1. Know the conditions for correlation and how to check them.
  2. Know that correlations are between -1 and 1, and that each extreme indicates perfect linear association
  3. Understand how the magnitude of the correlation reflects the strength of a linear association as viewed in a scatterplot
  4. Know that the correlation has no units
  5. Know that the correlation coefficient is not changed by changing the center or scale of either variable
  6. Know how to compute the correlation of two variables
*Text Reference: p.149, 152
2. Create a display (scatterplot) for the relationship between two variables
  1. Recognize when interest in the pattern of possible relationship between 2 quantitative variables suggests making a scatterplot
  2. Know how to identify the roles of the variables and to place the response variable on the y-axis and the explanatory on the x-axis
  3. Know how to make a scatterplot by hand(for a small set of data) or with technology
*Text Reference: p.146-149
3. Describe the relationship between two variables
  1. Be able to describe the direction, form, and strength of a scatterplot(relationship)
  2. Be prepared to identify and describe points that deviate from the overall pattern
  3. Be able to use correlation as part of the description of a scatterplot
  4. Be alert to misinterpretations of correlation
  5. Understand that finding a correlation between two variables does not indicate a causal relationship betwen them. Beware the dangers of suggesting causal relationships while describing correlations
  6. Understand that causation cannot be demonstrated by a scatterplot or correlation
  7. Know how to read a correlation table produced by statistical software
Extra Practice:
Chapter 7 Assessment external image vnd.openxmlformats-officedocument.spreadsheetml.sheet.png Ch. 7 1st Assessment Rubric.xlsx

Ch. 8: Linear Regression

1. Know how to find and use a regression equation for the relationship between two variables
  1. Be able to identify response(y) and explanatory(x) variables in context
  2. Understand how a linear equation summarizes the relationship between two variables
  3. Know how to find a regression equation from the summary statistics for each variable and the correlation between the variables
  4. Know how to find a regression equation using statistical software and how to find the slope and intercept values in the regression output table
  5. Know how to use regression to predict a value of y for a given x
2. Interpret a regression equation
  1. Be able to write a sentence explaining what a linear equation says about the relationship between y and x, basing it on the fact that the slope is given in y-units per x-unit
  2. Understand how the correlation coefficient and the regression slope are related.
  3. Know how r-squared describes how much of the variation in y is accounted for by its linear relationship with x
  4. Be able to describe a prediction made from a regression equation, relating the predicted value to the specified x-value

3. Recognize when a regression should be used to summarize a linear relationship between 2 quant. variables
  1. Be able to judge whether the slope of a regression makes sense
  2. Know how to examine your data for violations of the Straight Enough Condition that would make it inappropriate to compute a regression
  3. Understand that the least squares slope is easily affected by extreme values
  4. Know how to use a plot of residuals against predicted values to check the Straight Enough Condition or look for outliers

4. Calculate, interpret, and display residuals for each data value
  1. Know that residuals are the differences between the data values and the corresponding values predicted by the line and that the "least squares criterion" finds the line that minimizes the sum of the squared residuals
  2. Know how to compute the residual for each data value and how to display the residuals

Linear Regression Basics

Ch. 9: Regression Wisdom

1. Understand appropriate cautions to take when fitting a regression
  1. Understand that we cannot fit linear models or use linear regression if the underlying relationship between the variables is not itself linear
  2. Understand that data used to find a model must be homogeneous. Look for subgroups in data before you find a regression, and analyze each separately
  3. Know the danger of extrapolating beyond the range of the x-values used to find the linear model, especially when the extrapolation tries to predict into the future

2. Recognize and report any unusual points in a data set
  1. Understand that points can be unusual by having a large residual or by having high leverage
  2. Understand that an influential point can change the slope and intercept of the regression line
  3. Know how to look for high-leverage and influential points by examining a scatter-plot of the data and how to look for points with large residuals by examining a scatter-plot of the residuals against the predicted values or against the x-variable. Understand how fitting a regression line with and without influential points can add to understanding of the regression model
  4. Know how to look for high-leverage points by examining the distribution of the x-values or by recognizing them in a scatter-plot of the data, and understand how they can affect a linear model
  5. Report any high-leverage points
  6. Report any outliers. Consider reporting analyses with and without outliers included to assess their influence on the regression
3. Identify and discuss possible lurking variables
  1. Look for lurking variables whenever considering the association between two variables. Understand that a strong association does not mean that the variables are causally related

Linear Regression Advanced

Ch. 10: Re-expressing Data: Get It Straight!

1. Recognize when a well-chosen re-expression may help you improve and simplify your analysis
  1. Understand the value of re-expressing data to improve symmetry, to make the scatter around a line more constant, or to make a scatter-plot more linear
  2. Recognize when the pattern of the data indicates that no re-expression can improve the structure of the data
2. Find an effective re-expression of data and know how to re-express it with powers
  1. Know how to re-express data with powers and how to find an effective re-expression for your data using your statistics software or calculator
  2. Be able to reverse any of the common re-expressions to put a predicted value or residual back into their original units
  3. Be able to describe a summary or display of a re-expressed variable making clear how it was re-expressed and giving its re-expressed units
  4. Be able to describe a regression model fit to re-expressed data in terms of the re-expressed variables