4.5 linear regression ink.notebook. November 30, page 177 page Linear Regression. Standards. page 179. Lesson Objectives.
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1 4.5 linear regression ink.notebook page 177 page Linear Regression Lesson Objectives Standards Lesson Notes page Linear Regression Press the tabs to view details. 1
2 Lesson Objectives Standards Lesson Notes Lesson Objectives Standards Lesson Notes F.BF.1 I will write a linear function from a scatter plot using linear regression S.ID.6 I will use the graphing calculator and linear regression to find a linear equation from a scatter plot S.ID.8 I will use the graphing calculator to compute the correlation coefficient of a line of fit to a scatter plot Press the tabs to view details. S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. b. Informally assess the fit of a function by plotting and analyzing residuals. c. Fit a linear function for a scatter plot that suggests a linear association. S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. Press the tabs to view details. My Definition: A value that shows how close the data points are to a line Example: strong positive weak positive Characteristics: 1 or - 1 means all the dots are on the line. The closer to 1 a correlation is, the closer the data is to forming a straight line. Counterexample: Correlation Coefficient no correlation needs a scatter plot My Definition: a line that describes the tread of the data in a scatter plot Example: Line of Fit Characteristics: also called a trend line Counterexample: doesn't follow the trend 2
3 My Definition: an algorithm to find a precise line of fit for a set of data Example: a = 2 b = 1 y = 2x + 1 Linear Regression Characteristics: use the "stat" button on the graphing calculator Counterexample: Round to the nearest hundredth. 1. Years Since # of Radio Stations a) Find the equation: y = correlation: b) Using your equation, find out how many radio stations there were 35 years after (Let x = 35 in your equation and solve for y.) There were radio stations 35 years after 1970, in
4 4.5 linear regression ink.notebook 2. The following table list the wind chill factor, an indication of how cold it feels outdoors, for various temperatures (in F) when a 15 mi/h wind is blowing. Actual Air Temperature Wind Chill Factor a) Find the equation: y = correlation: b) Use your equation to predict the wind chill factor when the actual air is 35 and a 15 mi/h wind is blowing. (if x = 35, y =?) 3. The table below shows the number of cricket chirps for various air temperatures. Temperature ( F) Cricket Chirps per min a) Find the equation: y = correlation: b) The high temperature on a summer day reached 105 F. Use your equation to predict the number of chirps per minute at this temperature c = 4
5 On Your Whiteboards Using a graphing calculator, find the equation of the line of best fit. Then plug in x to find the missing y value. Round answers to the nearest hundredth. (.01) a) x y If x = 7, then y = b) x y On the Worksheet If x = 9, then y = 5
6 Find an equation that models the data in each scatter plot by hand. 1. slope = 2. slope = y = x + y = Homework 3. slope = y = Using a graphing calculator, find the equation of the line of best fit. Then plug in x to find the missing y value. Round answers to the nearest hundredth. (.01) 4. x y If x = 6, then y = 6
7 5. x y x y If x = 6, then y = If x = 5, then y = 7. x y If x = 8, then y = 8. x y If x = 7, then y = 7
8 9. x y Evaluate if x = 3, y = 4 and z = x 2 + 3y z 11. y 2 z If x = 6, then y = Translate each. 14. The sum of x and 8 Translate each times the difference of x and less than x 18. The product of n and The quotient of 3 and x 19. x is less than 7 8
9 20. Solve 2y = 6x 10 for y by showing all work Equation: 24. Equation: x =, m M = x =, m MNP = 9
10 25. Equation: Answers: x =, m BCD = 10
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