Ch 9

9.1 Use your calculator to find a regression equation for the line of best fit. Interpolation: using regression to make predictions within the data set Extrapolation: using regression to make predictions outside of the data set Predict the sales from the year 2000. Predict the sales from the year 2003. Predict the sales from the year 2010. Predict the sales form the year 2020. Predict the sales from the year 1900.

9.1 Plot the points (1,3) (-3,-7) and (5,7) on graph paper Connect point 1 to point 2 with a line Connect point 2 to point 3 with a new line Connect point 1 to point 3 with a new line Do any of these lines represent all 3 points well? Calculate a least squares regression line using the formula where a and b are parts of the slope intercept form: y=ax+b Does this equation represent all 3 points? Do pg 530-532

9.2 Correlation is how the data points relate to one another. A positive correlation is where y increases as x increases. A negative correlation is where y decreases as x increases. No correlation is where the data doesn’t seem related. Remember the correlation coefficient tells us how well the line fits the data. An r value close to 1 (positive correlation) or -1 (negative correlation) is a really good fit. An r value close to zero is a bad fit. Do pages 534-535 Calculate the correlation coefficient using the formula: Use the points (-3,-3) (1,2) and (3,4) as your data set. Do pg 539-540, 542-543 #1-5

9.3 A residual is the distance between an observed data point and one that is predicted by the linear regression equation (on the line). Observed Value – Predicted Value When a residual is positive, the actual data point is greater. When a residual is negative, the actual data point is less. You can plot residuals to determine what type of function is the best fit. If there is not pattern on the residual plot or if there is a flat (not increasing or decreasing) pattern in the residual plot, the data might be linearly related. If there is a different pattern, it’s probably not linearly related. Dp pg 547-551

9.5 Causation is where one event causes another. Correlation is where the two events are related. Correlation is necessary for causation, but not sufficient (not enough to prove the cause). A common response is where another reason could be causing the result. A confounding variable is where there are other unknown or unobserved variables. Do pg 564-567