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AP Statistics

Learn about regression conditions, standard error, confidence intervals, and t-tests to determine a linear relationship between rollercoaster drop height and speed using statistical analysis.

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AP Statistics

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  1. AP Statistics • Section 15.1: Regression Conditions

  2. Objective: To be able to determine if there is a significant linear relationship between two quantitative variables. Review Regression: Rollercoaster Data Set

  3. Points: • Our model is based on a sample. Therefore are statistics. • The model will vary from sample to sample. • The true model is . Where is the true mean response is the true slope (parameter) is the true y-intercept (parameter) Regression Conditions: • The responses for y are independent. (discuss) • There is a linear relationship between x and y. (scatterplot) • The errors have a constant variance. (residual plot) • The errors are normally distributed. (NPP of the residuals)

  4. Ex. 1 Check the conditions for inference for regression using the roller coaster data set.

  5. Standard Error about the LSRL: is the parameter which represents how the responses vary about the true regression model . We use the statistic s to estimate . • The larger s is the more spread out the points are about the linear model. • The reason we have (n-2) df is because we subtract one df for every parameter being estimated. Ex. 2 Calculate s for the rollercoaster data set.

  6. A Level C Confidence Interval for : where • Many times the values for or s are obtained from computer outputs. Ex. 3 Calculate a 95% confidence interval for the true slope of the regression line between rollercoaster drop height and speed.

  7. Linear Regression t-test: • Conditions: Stated previously (4) • Hypotheses: (there is no linear relationship between x and y) (there is a linear relationship between x and y) • Rejection Region: I will reject if my p-value < . OR I will reject if

  8. Test Statistic & p-value: 5. State your conclusion in the context of the problem. (2 parts)

  9. Ex. 4 Is there a significant positive linear relationship between drop height and speed for rollercoasters? THE END!

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