10.2 Regression By the end of class you will be able to graph a regression line and use it to make predictions.

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Presentation transcript:

10.2 Regression By the end of class you will be able to graph a regression line and use it to make predictions.

How Much Tip Should I Leave on a $41. 00 bill. ($33. 46, $5. 50) ($50 y=.1486x-.3472, tip = $5.75

Create a Scatterplot

Review of Linear Equations Graph the following linear equations:

Regression Line: The line of “best fit” for a scatter plot (minimizes the sum of the squares of vertical distances from each point to the line)

Line of Best Fit (Regression Line)

Regression Line:

On the Calculator: Column A: Independent Variable Column B: Dependent Variable Menu, stat, stat calc, linear regression

Making Predictions The sample is random Dependent Variable must be normally distributed about the regression line for each value of x

Making Predictions continued Standard deviation of each of the dependent variables must be the same for each value of x

So How much tip should I leave for a $41.00 check?

Extrapolation Extrapolation: Making predictions beyond the scope of data. Example: Some experts predicted $10/gal gas prices in the 1990s (was based on current oil reserves, not future)

Find the equation of regression line Age/Comfortable Sound Level (15, 56) (25, 57) (35, 64) (45 64) (55, 68) (65, 74) (75, 78) (85, 85) Find the equation of regression line Graph the scatter plot and regression line Predict the comfortable sound level for a 30 year old. y-=47.89x+.407, prediction = 60

Other Vocab Influential Point: An outlier that changes the regression line (pulls the regression line towards it) Marginal Change: The magnitude of change of one variable when the other variable changes by exactly 1 unit (the slope.)

Remember: Predictions are only made when the correlation is significant. Otherwise, the mean of the y’s (for that x value) is used to predict a value for y.

Hula Hoop How long would it take a hula hoop to pass through 30 people?