Regression inference confidence intervals


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Conditions & Regression Inference using Confidence Intervals

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Regression inference confidence intervals

  1. 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. 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. 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. 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.
  5. 5. Inference in Regression
  6. 6. Inference in Regression ^
  7. 7. Inference in Regression
  8. 8. Inference in Regression
  9. 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. 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. 11. Inference in Regression Helicopter Activity Computer Output: c. Interpret the confidence in context d. Interpret the meaning of “ 95% confident” in context.
  12. 12. Inference in Regression Pg. 749-750