invest_3ed.pdf

# For example newdata

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For example: > predict(lm(velocity~percentbodyfat), newdata= data.frame(percentbodyfat=25), interval="prediction") In Minitab x First run the model ( Stat > Regression > Regression > Fit Regression Model ). x Choose Stat > Regression > Regression > Predict and in the body fat table enter 25. x Press OK . x Report the interval listed under “95% PI.”

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Chance/Rossman, 2015 ISCAM III Investigation 5.13 396 (j) Report the 95% prediction interval for the takeoff velocity of a cat with 25% body fat from R/Minitab. Also determine the midpoint of this interval; does its value look familiar? Also interpret what this interval reveals. Prediction interval: Midpoint: Interpretation: (k) Repeat (j) to obtain a 95% prediction interval for the takeoff velocity of a cat with 50% body fat. Which interval is wider? Is this what you predicted in (i)? As you saw in Investigation 2.6, the level of precision will also depend on whether we want to predict the mean response or an individual response outcome. Definition: Statistical packages compute both “prediction intervals” and “confidence intervals.” A prediction interval gives us the interval of plausible values for an individual response at a particular value of the explanatory variable. A confidence interval gives us the set of plausible values for the mean response at a particular value of the explanatory variable. Technology Detour ± Confidence Intervals In R: use interval="confidence" In Minitab: Now report the 95% CI output. (l) What does R/Minitab report for the 95% confidence interval for the average takeoff velocity among all cats that have 25% body fat? Also determine the midpoint of this interval; does its value look familiar? Also interpret what this interval reveals. Confidence interval: Midpoint: Interpretation: (m) How does the interval in (l) compare to the interval in (j)? Why does this relationship make sense? Explain.
Chance/Rossman, 2015 ISCAM III Investigation 5.13 397 Study Conclusions Technology tells us that we are 95% confident that a cat with 25% body fat would have a takeoff velocity between 292.4 and 405.3 cm/sec. But if we were to consider the population of all cats with 25% body fat, we are 95% confident that the mean takeoff velocity of these cats is between 335.5 and 362.2 cm/sec, a much narrower interval. These procedures are valid because the analysis of the residual plots did not reveal any strong departures from the basic regression model conditions. Note: As with other t procedures, these procedures are fairly robust to the normality condition if you have a larger sample size except the prediction interval calculation. Practice Problem 5.13 Reconsider the 5K race results ( Talley5K2013.txt ) from Investigation 5.10. (a) Determine and interpret a 95% confidence interval for the mean finishing time of all 25-year-old runners in the population.

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