Conditions & Regression Inference using 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.
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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.

5. Inference in Regression

6. Inference in Regression
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7. Inference in Regression

8. Inference in Regression

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
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