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Simple Linear Regression

Simple Linear Regression. Section 13.1. Deterministic Relationship. If the value of y (dependent) is completely determined by the value of x (Independent variable) Most are not determined completely by another. Probabilistic Model.

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Simple Linear Regression

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  1. Simple Linear Regression Section 13.1

  2. Deterministic Relationship • If the value of y (dependent) is completely determined by the value of x (Independent variable) • Most are not determined completely by another

  3. Probabilistic Model • Description of the relation between 2 variables that are not deterministic. • It allows y to be larger or smaller than f(x) by a random amount, e. • Y = f(x) +e

  4. Let x* denote the value of x….

  5. Simple Linear Regression Model • Assumptions about the distribution of e • Mean • St. Dev. • Distribution of e at any x value is normal • Random deviations associated with different observations are independent of 1 another

  6. Slope • Average change in y associated with a 1 unit increase in x. • Point estimate is b. • Y-intercept’s point estimate is a.

  7. X* denotes a specified value of the predictor variable x …. • So has 2 different interpretations • It is a point estimate of the true mean y value when x = x*. • It is a point predictor of an individual y value that would be observed when x = x*.

  8. Find the point estimate of the mean y-value for the following: So what’s the point estimate for an 18 year old mom?

  9. Point estimate and point prediction are identical – only the interpretation is different. • Prediction – weight of single baby who mom is 18 • Estimate – average weight of all babies born to 18 year-olds

  10. Answer the following: • Explain the slope in context of the problem • Explain the y-intercept in context of the problem.

  11. Find SSResid. • on calculator – every time you calculate a linear regression – it calculates the residuals. Put them in list 3 and square them & add the list.

  12. Point estimate of is • It represents the typical deviation in the y-variable from the least squares line.

  13. Find the residual for a mother who is 19.

  14. Find the probability that a 19 year old mother has a baby that is more than 3000 g.

  15. Coefficient of determination (r2) • It’s the amount of variation in the y-variables that can be explained by the least squares line.

  16. Homework Worksheet

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