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Linear regression T-test

Linear regression T-test. Your last test !!. How good does this line fit the data?. What are some things that determine how good the line fits the data? R^2 The residual plot. Any obvious curvature in the data?. Conditions/Assumptions/requirements. I----each piece of data is independent.

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Linear regression T-test

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  1. Linear regression T-test Your last test !!

  2. How good does this line fit the data? • What are some things that determine how good the line fits the data? • R^2 • The residual plot. • Any obvious curvature in the data?

  3. Conditions/Assumptions/requirements • I----each piece of data is independent. • R---residual plot is randomly scattered and the residuals are normally distributed around the prediction line. • S---the data is a representative sample.

  4. Crying babies and IQ • If a baby doesn’t cry, what is their predicted IQ? • Explain the meaning of the slope in context of the problem. • What is the meaning of S? • What is the meaning of the correlation coefficient in terms of this problem? What is its value? • What is the meaning of coefficient of determination in this problem? What is its value?

  5. More questions • What is the standard deviation of the slope in this problem? What does it mean? • Is the slope a good fit for the data: use these Ho and Ha. What P-value do you use? • Ho: There is no association between crying and IQ scores (B=0) • There is an association between crying and IQ scores (B > 0)

  6. CI for the slope: • Using the data from the crying problem, give a 95% confidence interval for the slope of the problem. Formula is on next slide…..degrees of freedom is N-2 since any two point will make a line, so we discard 2.

  7. Blood alcohol content and Beer • One of the lines is with the outlier, one is without. Which is which?

  8. BAC and beers. • What is the slope of the LSRL for the relationship between BAC and beers drank? • If you have drank no beers, what is you predicted BAC? Is this reasonable? • Do you have confidence that the slope is accurate? What tells you this? • This answer is accurate under what conditions? (hint….IRS) • Do a 95% CI for the slope of the relationship between BAC and beers.

  9. More questions • What is the correlation coefficient for this question? What does it mean? • What is the coefficient of determination for this question? What does it mean? • What does the S mean?

  10. Icicle and time • The following data is from how long an icicle has to grow in minutes and how long the icicle becomes (in centimeters).

  11. Questions • What is the equation of the line that describes the relationship between time (minutes) and length of the icicle? • What is R? What’s it’s name? What does it mean? • What is R^2? What’s it’s name? What does it mean? • What does the S mean in context of the problem?

  12. Icicles and time • What does the slope mean in context of this problem? • What is a 95% Confidence Interval for slope of this equation? • Is the slope a good fit for the data? What tells you this? • What would Ho and Ha be for this problem? • What are the conditions be for us to make these statements?

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