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2.5 Notes Algebra II Date: __________________________________
Using Linear Models, Scatter Plots, and Regression Lines
Ex. On the first day of freshmen orientation this year, Marketplace Catering sold 45 candy bars o the 180 students that were here. The next day, both freshmen and sophomores were present (340 students total), purchased 85 candy bars. How many candy bars can Marketplace Catering expect to sell when all 800 students and faculty are at school?
Step 1 - Find two ordered pairs:
Step 2 - Find slope:
Step 3 - Write an equation in point-slope form:
Step 4 - Substitute into the linear equation to make predictions with the given value:
Ex. Health Department officials in San Mateo County are concerned with the West Nile virus. In a survey of a field with area of 10 square miles in Montara, they found 20 organisms with the virus. In a survey of a residential area in Foster City of 4 square miles, they found 8 infected organisms. If we develop a linear model to relate the area of a region to the number of organisms infected with this virus, what number of organisms would the Health Department predict that reside in San Mateo County (450 square miles).
Step 1 - Find two ordered pairs:
Step 2 - Find slope:
Step 3 - Write an equation in point-slope form:
Step 4 - Substitute into the linear equation to make predictions with the given value:
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|Scatter plot | |
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|Trend line | |
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|Guess price |Actual price |
|in thousand dollars |in thousand dollars |
|12 |11 |
|7 |8.5 |
|10 |12 |
|5 |3.8 |
|9 |10 |
Ex. An art expert visited a gallery and jotted down her guesses for the selling price of the five different paintings. Then, she checked the actual prices. The data points in the table show the results, where each number is in thousands of dollars.
A. Draw a scatter plot. Decide whether a linear model is reasonable.
B. Draw a trend line. Write the equation of the line.
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|Regression Line | |
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|Correlation | |
|Coefficient | |
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Ex. The table shows the life expectancy for people born in the United States. (Use Calculator)
|Year of Birth |Life Expectancy (yr)|
|1980 |73.7 |
|1983 |74.6 |
|1990 |75.4 |
|1995 |75.8 |
|2000 |76.8 |
|2006 |77.7 |
A. Make a Scatter Plot.
B. Find the equation of the line of regression. Interrupt in correlation coefficient.
C. Graph the regression line.
D. Predict the life expectancy of a person born in the United States in 2025.
Ex. The table to the right shows the average daily energy requirements for male children and adolescents.
|Age |Energy |
|(years) |Needed |
| |(Calories) |
| 1 |1100 |
|2 |1300 |
|5 |1800 |
|8 |2200 |
|11 |2500 |
|14 |2800 |
|17 |3000 |
A. Graph the data ON CALCULATOR.
B. Find the equation of the trend (regression) line. Interrupt in correlation coefficient.
C. Estimate the daily energy requirements for David, a 16 year old Serra student.
Ex. The numbering system used in Europe for shoe sizes is different from the system used in the United States. Use the data in the table at the right to create a model for converting between systems.
|U.S. shoe size |European size |
| 1 |31 |
|3 |34 |
|5 |36 |
|7 |39 |
|9 |41 |
|11 |44 |
A. Graph the data ON CALCULATOR.
B. Find the equation of the trend (regression) line. Interrupt in correlation coefficient.
C. Find the European equivalent of U.S. size 8.
Ex. The table shows population and licensed-driver statistics from a recent year. Is the population of a state related to the number of licensed drivers in that state?
|State |Population |Licensed Drivers|
| |(millions) |(millions) |
| Alabama | 4.3 |3.2 |
|Florida |14.7 |11.6 |
|Louisiana |4.4 |2.7 |
|South Carolina |3.8 |2.6 |
|Virginia |6.7 |4.7 |
|West Virginia |1.8 |1.3 |
A. Graph the data ON CALCULATOR.
B. Find the equation of the trend (regression) line. Interrupt in correlation coefficient.
C. The population of Oregon was approximately 3 million that year. About how many licensed drivers lived in Oregon that year?
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