SWBAT: Construct and Interpret a Confidence Interval for a Linear Regression Model Lesson 12-1 Do Now: 1. 2. 3. SWBAT: Construct and Interpret a Confidence Interval for a Linear Regression Model Lesson 12-1 Linear Regression Inference Conditions for Regression Inference Linear: Examine the scatterplot to check that the overall pattern is roughly linear. Look for curved patterns in the residual plot. C heck to see that the residuals center on the “residual = 0” line at each x-value in the residual plot. Independent: Normal: Make a stemplot, histogram, or Normal probability plot of the residuals and check for clear skewness or other major departures from Normality. Eq ual variance: Look at the scatter of the residuals above and below the “residual = 0” line in the residual plot. The amount of scatter should be roughly the same from the smallest to the largest x-value. Ra ndom: See if the data were produced by random sampling or a randomized experiment. Constructing a Confidence Interval for the Slope of the Regression Line statistic ± (critical value) · (standard deviation of statistic) ± ∗ In this formula, the standard error of the slope is = √ − SWBAT: Construct and Interpret a Confidence Interval for a Linear Regression Model Lesson 12-1 Confidence Interval for a Slope EXAMPLE: In C hapter 3, we examined data from a study that investigated why some people don’t gain weight even when they overeat. Perhaps fidgeting and other “nonexercise activity” (NEA) explains why—some people may spontaneously increase nonexercise activity when fed more. Researchers deliberately overfed a random sample of 16 healthy young adults for 8 weeks. They measured fat gain (in kilograms) and change in energy use (in calories) from activity other than deliberate exercise—fidgeting, daily living, and the like—for each subject. Here are the data: Minitab output from a least-squares regression analysis for these data is shown below. Construct and interpret a 90% confidence interval for the slope of the population regression line. SWBAT: Construct and Interpret a Confidence Interval for a Linear Regression Model Lesson 12-1 SWBAT: Construct and Interpret a Confidence Interval for a Linear Regression Model Lesson 12-1 You Try!! Do beavers benefit beetles? Researchers laid out 23 circular plots, each four meters in diameter, at random in an area where beavers were cutting down cottonwood trees. In each plot, they counted the number of stumps from trees cut by beavers and the number of clusters of beetle larvae. Ecologists think that the new sprouts from stumps are more tender than other cottonwood growth, so that beetles prefer them. If so, more stumps should produce more beetle larvae. Minitab output for a regression analysis on these data is shown below. C onstruct and interpret a 99% confidence interval for the slope of the population regression line. Assume that the conditions for performing inference are met. SWBAT: Construct and Interpret a Confidence Interval for a Linear Regression Model Lesson 12-1 LESSON PRACTICE 1. Here is one way in which nature regulates the size of animal populations: high population density attracts predators, which remove a higher proportion of the population than when the density of the prey is low. One study looked at kelp perch and their common predator, the kelp bass. The researcher set up four large circular pens on sandy ocean bottoms off the coast of southern C alifornia. He chose young perch at random from a large group and placed 10, 20, 40, and 60 perch in the four pens. Then he dropped the nets protecting the pens, allowing bass to swarm in, and counted the perch left after two hours. Here are data on the proportions of perch eaten in four repetitions of this setup: We used Minitab software to carry out a least-squares regression analysis for these data. A residual plot and a histogram of the residuals are shown below. C omputer output from the least-squares regression analysis on the perch data is shown below. C onstruct and interpret a 90% confidence interval for the slope of the true regression line. SWBAT: Construct and Interpret a Confidence Interval for a Linear Regression Model Lesson 12-1 2. How well does the number of beers a person drinks predict his or her blood alcohol content (BAC )? Sixteen volunteers with an initial BAC of 0 drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their BAC . Least-squares regression was performed on the data. A residual plot and a histogram of the residuals are shown below. C omputer output from the least-squares regression analysis on the beer and blood alcohol data is shown below. C onstruct and interpret a 99% confidence interval for the slope of the true regression line.
© Copyright 2026 Paperzz