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.

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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.  R---residual plot is randomly scattered and the residuals are normally distributed around the prediction line.  S---the data is a representative sample.

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?

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)

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.

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

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.

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?

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).

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?

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?