Lesson 2: 4.2 Least Squares Regression

• How do I make predictions using regression lines, keeping in mind the dangers of extrapolation?
• How do I calculate and interpret a residual?
• How do I interpret the slope and y intercept of a least-squares regression line?
• How do I determine the equation of a least-squares regression line using technology or computer output?
• How do I construct and interpret residual plots to assess whether a regression model is appropriate?
• How do I interpret the standard deviation of the residuals and r2 and use these values to assess how well the least-squares regression line models the relationship between two variables?
• How do I describe how the slope, y intercept, standard deviation of the residuals, and r2 are influenced by unusual point?
• How do I find the slope and y intercept of the least-squares regression line from the means and standard deviations of x and y and their correlation?

- regression line
- extrapolation
- residual
- y-intercept
- slope
- least-squares regression line
- residual plot
- standard deviation of residuals, s
- the coefficient of determination, r2
- high leverage, outlier, influential point

ID.B.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
ID.B.6.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.  
ID.B.6.b: Informally assess the fit of a function by plotting the residuals.
ID.B.6.c: Fit a linear function to data using technology, and interpret the slope and intercept. Fit a linear function to data using technology, and interpret the slope and intercept. For scatter plots that suggest a linear association, informally determine a line of best fit.
ID.B.6.d: Interpret the slope and intercept of a linear model in the context of the data.

These skills are essential for understanding and applying linear regression, a statistical method used to model the relationship between a dependent variable and one or more independent variables.

By mastering these skills, you can effectively use linear regression to analyze data, make predictions, and draw meaningful conclusions.

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