Estimating the Slope of a Least-Squares Regression Line (Lesson 11.5)
Chapter 11 - Day 7
Learning Targets
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Check the conditions for inference about the slope of a least-squares regression line.
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Calculate a C% confidence interval for the slope of a least-squares regression line.
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Use the four-step process to construct and interpret a confidence interval for the slope of a least-squares regression line.
Experience First
Our final topic for the course is about inference for slope. In Lesson 11.5 we calculate and interpret a confidence interval for slope and in Lesson 11.6 we test a claim made about slope. We will use the same context for both lessons.
These final two lessons in Chapter 11 are a great opportunity to review some ideas from the two-variable data analysis we did in Chapter 3, including making scatterplots and residual plots, finding the equation of the line of best fit, and interpreting slope.
Students will use the Linear regression t interval applet (part of the Traditional Inference applets at www.statsmedic.com/applets). Students can use this applet at the beginning of the activity to find the equation of the line of best fit, and also the end of the activity to check conditions and calculate a confidence interval.
Formalize Later
When debriefing the activity, here are a few items to highlight:
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When defining the parameter, it is important to include context. We do this by stating the two variables.
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There are 4 conditions to check! The applet will help you with the three graphs you need (scatterplot, residual plot, and dotplot of residuals). We suggest you don't get too far into the weeds with these conditions.
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Remember that a confidence interval gives a list of plausible values for the parameter. In this activity, it is plausible that moving one row further back will reduce a predicted student score by between 4.525 and 6.58 points.
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Because the confidence interval does not contain 0, it is not plausible that there is no linear relationship between row (x) and score (y). We will formally test this claim in Lesson 11.6.
Because we skipped the calculation and allowed students to use the applet to get the confidence interval, the discussion about degrees of freedom is not needed. For those interested, the degrees of freedom for regression inference is df = n - 2, where n is the sample size.