AP Statistics · Summary

Unit 5 summary

  1. Describe a scatterplot by direction, form, strength and unusual points, always naming both variables.
  2. r measures only linear relationships, has no units, ignores which variable is x, and is not resistant. Correlation does not show cause.
  3. The least-squares line y^=a+bx\hat{y} = a + bx has b=rsysxb = r \frac{s_y}{s_x} and passes through (xˉ,yˉ)(\bar{x}, \bar{y}).
  4. Slope: the predicted change in y for each 1-unit increase in x. Intercept: the predicted y at x = 0, often not meaningful.
  5. Residual = observed - predicted. Positive means the line underpredicted.
  6. A residual plot with random scatter supports a line; a curve or fan signals a problem, whatever r-squared is.
  7. r-squared is the share of the variation in y accounted for by the linear relationship with x. Do not predict outside the range of x.