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Cal Poly STAT 217 - Regression

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Winter, 2010Stat 217 – Regression (Topics 26, 27, 28, 29)For this topic, we will discuss how to analyze the relationship between two quantitative variables. (So no longer about differences between groups but instead the association between variables.) As with other analyses, we will first learn appropriate descriptive statistics (graphical and numerical summaries) and then consider models for the data (can we summarize the relationship in a simple way, that helps with predictions – the analogy here is the normal model which allowed us to predict the values of the middle 68% or middle 95% of the distribution), and then proceed to inferential statistics which allow us to draw conclusions about a larger population or process based on the sample data. As always, the inferential analysis will ask how likely we are to observe a relationship like we did if there is no real relationship in the population/process.Example 1: House Prices1) Graphical summaryActivity 26-1 (p. 532)What to remember: - How to create a scatterplot in Minitab (response vs. explanatory), see Lab 9- How to describe scatterplots in terms of direction, strength, and form.2) Numerical summary: Use the correlation coefficient, r, to measure the strength of the relationship instead of relying on our visual impressions. Values of r close to -1 or 1 indicate a stronger linear relationship, close to zero indicate no linear relationship. Be cautious in looking at the scatterplot first, making sure it is linear before you interpret r. What to remember:- The correlation coefficient only measures linear association- Sign of r tells you about direction of association as well.3) Model: Least Squares Regression Activity 28-1 (p. 575) What to remember:- “Least Squares Regression” minimizes the sum of the squared residuals- Interpretations of slope and intercept (p. 577)- Using the regression line to make (reasonable) predictions- Using Minitab to obtain a regression line, superimpose on scatterplot (visually judge how well line summarizes the data)Graph > Scatterplot > With Regression Graph > Regression > Fitted Line Plot Mouse over line to see equation = a + bxWinter, 20104) Statistical inference (p. 605)Let - represent the population regression line slopeH0: - = 0 (no relationship between response variable and explanatory variable)Ha: - <, >, 0 (is a negative, positive, a relationship between the variables)Technical conditions: Linear relationship, random sample, and othersSkip Activity 29-2: use of residual plots to check technical conditions.Test statistic: t = (observed slope – hypothesized slope)/SE(b)Where SE(b) represents the sample to sample variation in the regression slopes df = n -2p-value: note that Minitab always finds a two-sided p-valueYou can cut it in half if your Ha is one-sided and b is the right signActivity 29-3 Stat > Regression > RegressionWinter, 2010The regression equation isPrice = 265222 + 169 Size (sq ft)Predictor Coef SE Coef T PConstant 265222 42642 6.22 0.000Size (sq ft) 168.59 31.88 5.29 0.000Winter, 2010Example 2: Textbook Prices (28-4, 28-5)What factors are related to the price of college textbooks? (Shaffer and Kaplan, 2006)Winter, 2010The regression equation is Price = - 3.4 + 0.147 PagesPredictor Coef SE Coef T PConstant -3.42 10.46 -0.33 0.746Pages 0.14733 0.01925 7.65 0.000 The regression equation isPrice = - 4969 + 2.52 YearPredictor Coef SE Coef T PConstant -4969 1990 -2.50 0.019Year 2.5162 0.9946 2.53 0.017Winter,


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Cal Poly STAT 217 - Regression

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