6.3 Modelling Data with Lines of Best Fit
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1 6.3 Modelling Data with Lines of Best Fit GRADE (%) Number of Absences The independent variable: is the variable that is being manipulated. variable goes on the x axis of graph The dependent variable: is the variable that is being observed. The dependent variable goes on the y axis 1
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5 Variable - ( y values) (goes on y axis) A variable whose value is determined by the values of another variable. ( variable) Variable - ( x values) (goes on x axis) A variable whose value is NOT determined by the values of another variable and whose value determines the value of the dependent variable. 1. Height of Ferris wheel ride over time 2. The number of cars in school parking lot over time 3.Temperature of water in freezer over time 4. The odometer reading in the car over time 5. The equation V= 0.08d+8 represents the volume of gas (V litres) remaining in the tank after travelling d kilometers 6. Cameron works for a research company in a shopping mall. The equation P=5n+30 represents her daily pay, P dollars, when she conducts n surveys. 7. The equation C=0.10m+8 represents the cost, for a monthly cell phone plan with Dogers Mobility after m minutes of talking on the phone. 8. The equation C= 0.10d+4 represents the cost, C, dollars for a taxi cab ride in Charlottetown travelling over a certain distance, d kilometers 9. The amount of tension on a guitar string determines the musical not played 10. The amount of money made at bake sale and the number of bake goods 11. Level of music and amount of hearing loss 12. plant growth and sunlight hours 13 Effect of studying time on test marks 14. Distance travelled and cost of plane ticket 5
6 Line of best fit: A straight line that best approximates the trend in a scatter plot. (hand drawn) Regression function: A line or curve of best fit, developed through a statistical analysis of data. (calculator will do this) Interpolation the process used to estimate a value within the domain of a set of data, based on a trend. Extrapolation the process used to estimate a value outside the domain of a set of data, based on a trend. 6
7 6.3 Modelling Data with Lines of Best Fit GRADE (%) Number of Absences LINE OF BEST FIT: A straight line that best approximates the trend in the scatter plot (hand drawn). The line should have approximately equal number of data points both above and below the line. REGRESSION FUNCTION: A line or curve of best fit, developed through statistical analysis of data (calculator will do this). INTERPOLATION: The process used to estimate a value within the domain of a set of data, based on a trend EXTRAPOLATION: The process used to estimate a value outside the domain of a set of data, based on a trend. The independent variable: is the variable that is being manipulated. variable goes on the x axis of graph. A variable whose value is NOT determined by the values of another variable and whose value determines the value of the dependent variable. The dependent variable: is the variable that is being observed. The dependent variable goes on the y axis of graph. A variable whose value is determined by the values of another variable. 7
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10 89 d. Predict the mass of a trainee whose height is 179 cm. Round answer to nearest whole number (use graph and equation) e. Predict the height of a 80 kg trainee. Round off the answer to the nearest whole number (use graph and equation) 10
11 Use equation and graph to get answer b) Predict how many horses a stable of 2846 ft 2. Round to nearest horse. Use equation and use graph to check answer (see right board) 11
12 The provincial government plans to buy 500 winter parkas with goose down for park rangers. One office supplier offers these prices Number of Parkas Cost for each ($) a) Use linear regression to find the equation of the line of best fit for the data. y = 0.38x+433 b) What price should the government expect to pay for each of the 500 parkas? How much each for 450 parkas? c) How many parks would the government need to order for each parka to cost $360 each? 12
13 Danielle, a real estate agent, helps businesses move to new offices. If an office does not have enough area, the employees will not be able to work productively. If there is too much area, the business will pay too much rent. One client is a business that has 14 employees. Danielle has made the following table about other businesses in one building number of employees Office space (m2) a) Use linear regression to find the equation of the line of best fit b) What area of office space should she look for to fit 14 employees? Round to nearest tenths place c) Danielle has found an office that is cm 2. How many employees could work comfortably in this space? 13
14 The winning times for the women's 100 m freestyle swim in the Summer Olympics for most years from 1984 to 2008 are shown Year Winning Time (s) a) Use linear regression to determine the equation for the line of best fit for the data b) Determine a possible winning time for the event in the 1996 Summer Olympics Compare your estimate with the actual winning time of 54.50s 14
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16 Sec 6.4 Modelling Data with a Curve of Best Fit curve of best fit a curve that best approximates the trend on a scatter plot c. Predict the height of a tree whose area covered 10.0 m 2. Round answer to on decimal place 16
17 b) Determine the cubic regression equation that models the data. Use your equation to estimate the average price of gas in 1984 and c) Estimate the year in which the average price of gas was 65.0 cents per litre 17
18 d) When does the pebble reach 5 m? 18
19 e) when did the ball reach 12 m? 19
20 d) Estimate the day when the mass of bacteria reaches 15 g. 20
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