Regression inference confidence intervals
- 1. Focus Fox What is a regression line? What is the equation of a regression line in variables? What is a residual? What is a residual plot? What is a normal probability plot?
- 2. Inference in Regression Population regression line uses all the observations. µ = α + βx Sample regression line (estimated regression line) uses only the observations in a SRS. y = a + bx Sampling distribution of b – slope Shape: distribution roughly symmetric, Normal Probability Plot (z- score) is linear – close to Normal Center: mean of sampling distribution is close to slope of population regression line Spread: standard deviation of sampling distribution is close to actual standard deviation in population. ^
- 3. Inference in Regression Conditions for Regression Inference - 5 Linear: examine scatterplot to check overall pattern is roughly linear, residuals should center on 0, look for curved pattern in residual plot Independent: look for random assignment or experiment, if sampling without replacement – check 10% condition Normal: make a stemplot, histogram, or Normal probability plot of residuals and check for skewness or departure from Normality Equal Variance: the scatter in the residuals (above and below the line) should be roughly the same Random: were the data produced by random sampling or random assignment
- 4. Inference in Regression Mrs. Barrett’s class did an experiment dropping helicopters from various heights. 14 helicopters at each of 5 drop heights in centimeters. Teams of students released the 70 helicopters in a predetermined random order and measured the flight times in seconds. The class used Minitab to carry out a least-squares regression analysis for these data. A scatterplot, residual plot, histogram, and Normal probability plot of the residuals are on the next slide. Check whether the conditions for performing inference about the regression model are met.
- 9. Inference in Regression Helicopter Activity Computer Output: a. Identify the standard error of slope SEb from the computer output, interpret this value in context.
- 10. Inference in Regression Helicopter Activity Computer Output: b. Find the critical value for a 95% confidence interval for the slope of the true regression line. Then calculate the confidence interval.
- 11. Inference in Regression Helicopter Activity Computer Output: c. Interpret the confidence in context d. Interpret the meaning of “ 95% confident” in context.
- 12. Inference in Regression Pg. 749-750