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Linear regression T-test Your last test !!

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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?

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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.

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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?

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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)

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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.

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

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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.

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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?

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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).

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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?

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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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STA 286 week 131 Inference for the Regression Coefficient Recall, b 0 and b 1 are the estimates of the slope β 1 and intercept β 0 of population regression.

STA 286 week 131 Inference for the Regression Coefficient Recall, b 0 and b 1 are the estimates of the slope β 1 and intercept β 0 of population regression.

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