2. Aim: Line of Best Fit Course: Alg. 2 & Trig. Aim: How do we use data to make predictions – (linear regression)? Do Now: A candle is 6 inches tall after burning for 1 hour. After 3 hours, it is 5 ½ in. tall. Write a linear equation to model the height y of the candle after burning x hours. point-slope form. (1, 6) (3, 5.5) slope is the rate of change

3. Aim: Line of Best Fit Course: Alg. 2 & Trig. Do Now Extension Do Now: A candle is 6 inches tall after burning for 1 hour. After 3 hours, it is 5 ½ in. tall. (1, 6) (3, 5.5) In how many hours will the candle be 4 inches tall? y - height of candle x - hours. x = 9 hours (4, 9)

4. Aim: Line of Best Fit Course: Alg. 2 & Trig. Interpreting Data The cost of attending college is steadily increasing. The chart shows the average tuition and fees for a full-time resident student at a public four-year college. Estimate the average college cost in the academic year beginning in 2007 if tuition and fees continue at this rate. YearTuition & Fees YearTuition & Fees 1990-9121591995-962811 1991-9224101996-972975 1992-9323491997-983111 1993-9425371998-993243 1994-952681

5. Aim: Line of Best Fit Course: Alg. 2 & Trig. Finding Best Fit Equation Average Tuition and Fees 3500 1700 1900 2100 2300 2500 2700 2900 3100 3300 1990 19911992199319941995199619971998 (1992, 2349) (1997, 3111) Select 2 points that represent the data Determine slope Calculate equation of best fit line

6. Aim: Line of Best Fit Course: Alg. 2 & Trig. Scatter Plots & Correlation A Scatter Plot is a graph that relates two different sets of data by plotting the data as ordered pairs. Positive Correlation y tends to increase as x increases slope is positive Negative Correlation y tends to decrease as x increases slope is negative No Correlation

7. Aim: Line of Best Fit Course: Alg. 2 & Trig. Correlation Co-efficient Data that are linear in nature will have varying degrees of goodness of fit to the lines of fit. The correlation coefficient r describes the nature of data. The closer the fit of the data to the line, the closer r gets to + 1 or -1 0 < r < 0.5 positive/weak 0.75 < r < 1 strongly positive -0.5 < r < 0 moderately negative

8. Aim: Line of Best Fit Course: Alg. 2 & Trig. Making Predictions Projected cost in 2006-2007 Predict cost for 2006-2007 academic year by substituting 2006 for x in best fit equation. Prediction: cost for tuition and fees will be $4482.60 Trend line – approximates the relationships between data sets of a scatter plot.

9. Aim: Line of Best Fit Course: Alg. 2 & Trig. Least Squares Regression Line The least square regression line, y = ax + b, for the point (x 1, y 1 ), (x 2, y 2 ), (x 3, y 3 ), ….. (x n, y n ) is given by How can we find an equation that fits the data more closely if the correlation is not very high? Thank you TI 83+!!

10. Aim: Line of Best Fit Course: Alg. 2 & Trig. Using Graphing Calculator to Determine Equation of Best Fit. Enter years into L 1 Enter dollars into L 2 STAT 1 1 Ensure coordinate pairs correspond Enter data:

11. Aim: Line of Best Fit Course: Alg. 2 & Trig. Using Graphing Calculator to Determine Equation of Best Fit.  ENTER STAT 4 Calculate the regression line: 2nd Graph results: Y = ENTER ZOOM 9 ENTER

12. Aim: Line of Best Fit Course: Alg. 2 & Trig. Using Graphing Calculator to Determine Equation of Best Fit.  ENTER STAT 4 Graph the regression line: VARS  1 ENTER GRAPHTRACE

13. Aim: Line of Best Fit Course: Alg. 2 & Trig. 6 pt. Regents Question The availability of leaded gasoline in New York State is decreasing, as shown in the accompanying table. Determine a linear relationship for x (years) versus y (gallons available), based on the data given. The data should be entered using the year and the gallons available (in thousands), such as (1984, 150) YEAR19841988199219962000 Gallons Available (in thousands) 1501241047650

14. Aim: Line of Best Fit Course: Alg. 2 & Trig. 6 pt. Regents Question The availability of leaded gasoline in New York State is decreasing, as shown in the accompanying table. If this relationship continues, determine the number of gallons of leaded gasoline available in New York State in the year 2005. YEAR19841988199219962000 Gallons Available (in thousands) 1501241047650

15. Aim: Line of Best Fit Course: Alg. 2 & Trig. 6 pt. Regents Question The availability of leaded gasoline in New York State is decreasing, as shown in the accompanying table. If this relationship continues, during what year will leaded gasoline first become unavailable in New York State? YEAR19841988199219962000 Gallons Available (in thousands) 1501241047650

16. Aim: Line of Best Fit Course: Alg. 2 & Trig. Model Problem The table contains the fat grams and calories in various fast-food chicken sandwiches. a.Find the equation of the regression b.Predict the number of calories in a sandwich with 20 grams of fat. Sandwichfat (grams) caloriesSandwichfat (grams) calories A breaded 28536G breaded 9300 B grilled 20430H ch. salad 5320 C ch. salad 33680I breaded 26530 D broiled 29550J breaded 18440 E breaded 43710K grilled 8310

17. Aim: Line of Best Fit Course: Alg. 2 & Trig.