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CH 27

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* Data were collected on 208 boys and 206 girls. Parents reported the month of the baby’s birth and age (in weeks) at which their child first crawled. The table gives the average temp when the babies were 6 months old. Birth Month 6-mos Temp Avg Crawl Age Jan6629.84 Feb7330.52 Mar7229.70 Apr6331.84 May5231.65 Jun3931.44 Jul3333.64 Aug3032.82 Sep3333.83 Oct3733.35 Nov4833.38 Dec5732.32

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* How do we make a scatterplot? * What do we look for in a scatterplot? * How do we find the correlation? * What does the correlation mean * What does r-squared mean? * How do we create a linear model? * How do we know if the linear model is appropriate? * How do we create a residual plot? * What do we look for in the residuals plot? * What does the slope mean? * What does the y- intercept mean?

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* The test for independence allowed us to check for evidence of an association between CATAGORICAL variables. * A Regression Slope t- test allows us to check for evidence of an association between QUANTITATIVE variables.

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You will most likely not have to actually check these conditions. They will either be confirmed for you, or information will be provided to help you quickly check through them. You do need to know them.

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Check this by showing a scatterplot. You can eyeball this condition and say, ‘The scatterplot appears to be linear.’

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We want to make sure that one subject’s longer- than-expected time to crawl does not tell whether another baby might take longer or shorter to crawl than the temp might predict. You can check this by showing a residual plot and confirming that the residuals have a random scattering.

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The variabilility of y should be about the same for all values of x. (side note : this is called homoscedasticity) Basically, we are trying to see if the y’s have equal variance. You can check this by seeing if your residual plot trumpets out.

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We are seeing if the errors around the idealized regression line at each value of x follow a Normal model. We check this by looking at a histogram or Normal probability plot of the residuals

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1. State the conditions. 2. Name the test. 3. State the hypotheses. 4. Give the test statistic, df, and pvalue. 5. Conclusion in context.

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* Run a LinRegTTest on your data to produce these results for step 3. * t=-4.67, df = 10, pvalue = approx 0 * pvalue < alpha. 0 < 0.5. therefore, we have significant evidence to reject the null that there is no relationship between temperature and crawling age in favor of the alternate hypothesis that there is a relationship (association) between temp and crawling age.

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* Regression Slope t-interval * Conditions met as stated before. * Run the interval on your calc to get these results. * (-0.1119, -0.0396) * I am 95% confident that babies are predicted to take between 0.0396 and 0.1119 weeks longer to crawl for every degree increase in 6 month temperature.

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Please take time to read ch 27. Make sure to go over the ti tips for the calculator and the section that describes computer print out.

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