1. Chapter 14, continued More simple linear regression Download this presentation.

2. III. B. The Least-Squares Criteria The least squares method was proposed by Carl Friedrich Gauss (1777-1855), a brilliant German mathematician and astronomer. In fact, he did some work in Hanover!Carl Friedrich Gauss (1777-1855), That’s Hannover Germany, you nitwit!Hannover Germany Sorry, big guy!

3. The Method The procedure is to find b 0 and b 1 to minimize the sum of the squared deviations between y i and. Performing this minimization will produce the equations below.

4. Necessary Calculations

5. Solve for the parameter estimates b 0 = 276 - (75.50)(3) = 49.50 So what does it mean, Einstein?

6. Interpretations b 1 =75.50 means that for every additional year of a car’s age, repair cost will rise by $75.50. b 0 =49.50 means that if a car is zero years old (x=0), the repair cost would be $49.50. We shouldn’t put too much emphasis in the interpretation of b 0. It acts as a sponge, capturing many other effects on the dependent variable and is thus unreliable for much explanatory power.

7. Using the regression equation. We can use the estimated equation to predict the repair cost of a 5-year old car. So if x=5, =$427. But a 5-year old car in the sample only cost $450 to repair! How come my estimate is off by $23?!!? Knowing you, you probably messed something up.

8. Of course our estimates of repair cost don’t equal the actual values because the world doesn’t usually behave in a perfectly linear way. You can see that the estimated regression line doesn’t go through all of our data points. But there are some points that are closer to the line than others, which implies some kind of margin of error. The next section will develop a tool for measuring how well our equation fits the data.