Key Takeaways

  • The parameter \(β_1\), the slope of the population regression line, is of primary interest because it describes the average change in \(y\) with respect to unit increase in \(x\).

  • The statistic \(\hat{\beta}_{1}\), the slope of the least squares regression line, is a point estimate of \(β_1\). Confidence intervals for \(β_1\) can be computed using a formula.

  • Hypotheses regarding \(β_1\) are tested using the same five-step procedures introduced in Chapter 8 "Testing Hypotheses".