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.

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Presentation transcript:

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

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)

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

Aim: Line of Best Fit Course: Alg. 2 & Trig. Finding Best Fit Equation Average Tuition and Fees (1992, 2349) (1997, 3111) Select 2 points that represent the data Determine slope Calculate equation of best fit line

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

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

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

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+!!

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:

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

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

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) YEAR Gallons Available (in thousands)

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 YEAR Gallons Available (in thousands)

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? YEAR Gallons Available (in thousands)

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 D broiled 29550J breaded E breaded 43710K grilled 8310

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