Section 3. Simple Regression (One Regressor)1. Introduction: Fitting a Line through a cloud2. Coffee example3. Global Warming example4. CA test score example5. Stata in action6. Which line to choose?7. What’s to come?8. Population Regression Line4-21. Introduction: Fitting a Line through a Cloud• e.g. Demand for Coffee, Global warming, CA test scores and student-teacher ratios• Why is drawing lines useful?Describing dataTesting hypothesesPrediction• Which line to chose? Minimizing “residual” or “error” terms ui• Note: slope and intercept are random variables• Note: It’s usually the population we care about4-32. Coffee Demand againcups of coffeeprice per cup01 2 30501001504-42. Coffee Example (in logarithms)lqlp-1-.5 0 .5 1012344-52. Coffee example (with a line)What’s the slope of the line?About how many cups would you sell at $1?lp lq Fitted values-1-.5 0 .5 1012344-62. Coffee example (with a curve)Predicted values qhat = exp(lqhat)About how many cups would you sell at $1?price per cup cups of coffee qhat01 2 30501001504-73. Global Warming ExampleEarth's temperature since 1880year18801993-1.2.8Is the slope statistically different from zero?4-84. CA Test Score Example4-94-105. Stata in Action• Stata example4-116. Which line to choose?“Error terms”4-127. What’s to come?• Decide which parameters in population we care about (β0,β1) - just like we did with µ• Draw a sample and estimate parameters- just like we did with µ• Construct CI for parameters, test hypotheses, make predictions.-just like..4-138. Population regression line: terms4-14Next time..• Estimators for intercept β0and slope β1• Confidence intervals for β0, β1Lesson #5: Simple Regression (One Regressor)1. Introduction: Fitting a Line through a cloud2. Cereal bars example3. Global Warming example4. CA test score example5. Stata in action6. Which line to choose?7. What’s to come?8. Population Regression Line4-16Appendix
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