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Common Core Math 1Day 6 – Classroom Notes –Scatter Plots and LINE of BEST FIT
I. Vocabulary
Scatter Plot- Trend Line- No Correlation-
Positive Correlation- Negative Correlation- Strong or Weak Correlation-
Line of Best Fit- Linear Regression or LinReg (on calculator)
Linear Extrapolation- Linear Interpolation-
II. Scatter PlotsExamples – Determine if the following Scatter Plots have Positive Correlation, Negative Correlation or No Correlation
III. ReasoningQuestion: Why do we use Best Fit Lines? To __________ data given a set of data.
IV. Line of Best FitExample 1 – The table shows an estimate for the number of bald eagle pairs in the United State for certain years since 1985.
a) Find the Line of Best Fit
b) Estimate the number of Bald Eagle pairs in 1998.
Example 2 – The table shows the world population growing at a rapid rate.a) Write an equation in slope-intercept form that best represents this data.
b) What is the world population in 2010?
Example 3 – The table shows the length and weight of several humpback whales.
a) What is the Line of Best Fit for the data. b) What is the weight of a 48-foot humpback whale?
Example 4 – The table shows the average body temperature in Celsius of 9 insects at a given air temperature.
a) Write the linear equation for the best-fit line. b) Predict the body temp of an insect when air temp is 40.2 F
Example 5 – The table shows the amount of money the US spent on NASA in specific years.
a) Write a line of fit equation where x represents the years since 1980 and y represents the US spending
b) Predict the amount that will be spent in 2005.
c) In 2005, $14.3 billion was actually spent on NASA. How does this compare to your prediction?
d) Predict the amount that will be spent in 1961 when JFK declared his goal to put a man on the moon.
Example 6 – The table shows the average hourly earnings of US production workers for selected years.
a) Write an equation for line of best fit with x representing years since 1960.
b) Predict the average earnings in 1930, when the Great Depression hit the US. Interpret if this is a good prediction. Why?
c) Predict the average earnings in 2010?
V Practice Find an equation for the line of best fit, make the corresponding predictions, explain what the slope represents, and explain what the y-intercept represents.
1)Year Cost of Stamp1958 0.041963 0.051968 0.061971 0.081974 0.101975 0.131978 0.151981 0.181985 0.221988 0.251991 0.291995 0.32
i. Equation of line of Best Fit:_______________
ii. Predict cost of stamp in 2000:_____________
iii. Slope represents:______________________
iv. y-intercept represents:__________________2)
Weight(tons) Miles Per Gallon1.3 291.4 241.5 231.8 212.1 172.4 15
i. Equation of line of Best Fit:_______________
ii. Predict the Miles per Gallon for a weight of 1.7 tons:__________________________
iii. Slope represents:______________________
iv. y-intercept represents:__________________
3)Year Trash (millions
of tons)1960 881965 1031970 1221975 1281980 1521985 1641990 196
i. Equation of line of Best Fit:_______________
ii. Predict Trash in 2010:___________________
iii. Slope represents:______________________
iv. y-intercept represents:__________________
4)Length Weight (long tons)
40 2542 2945 3446 3550 4352 4555 51
i. Equation of line of Best Fit:_______________
ii. Predict weight for a length of 60:__________
iii. Slope represents:______________________
iv. y-intercept represents:_________________
VI. Word Problem Examples
1. A package containing 2 Reese’s cups costs 60 cents. A package containing 10 Reese’s’ cups costs $2.40.
a) Find a prediction equation that relates the number of cups and the cost (make 2 ordered pairs).
b) Approximately how many Reese’s cups could Jim buy for $10?
c) Predict the cost of 100 Reese’s cups.
d) What does the slope represent?
e) What does the y-intercept represent?
2. According to a certain linear prediction equation, the cost of 200 square feet of storage space is $60. To cost of 325 square feet of storage space is $160.
a) Find the prediction equation.
b) Predict the cost to rent 500 square feet f storage space.
c) Predict the number of square feet Ashley can rent for $44.
3. At Wendy’s, a single hamburger cost $0.99. A double hamburger cost $1.49. Assuming this relationship is linear, predict the cost of a triple hamburger.
VII. Extension - HomeworkNews Reporters
The following chart lists the number of influenza-like illnesses reported in North Carolina from Sunday, August 23, 2009 through Saturday, October 10, 2009. (epi.state.nc.us)
Week Ending Week of the Year Influenza-Like Illness8/29/09 34 4209/5/09 35 16359/12/09 36 27869/19/09 37 41879/26/09 38 550610/3/09 39 666210/10/09 40 7894
1. What is the independent variable? Why? ______________________________________________
2. What is the dependent variable? Why? _______________________________________________
3. What is the linear regression equation for the data? _____________________________________
4. What is your interpretation of the slope (complete sentence)? ____________________________________________________________________________________________________________
5. What is your interpretation of the y-intercept (complete sentence)?________________________________________________________________________________________________________
6. Use your prediction equation to predict how many influenza-like illnesses were reported during the week of Christmas. (week 52)
7. List some of the factors that could influence the validity of your answer for question 6.
8. Write a news report consisting of at least four sentences that uses the results that you found in your investigation.
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The following chart lists the career saves of Mariano Rivera, pitcher for the New York Yankees. (sports.yahoo.com) Let 1990 = 0
Year Career Saves1995 01996 5
1997 481998 841999 1292000 1652001 2152002 2432003 2832004 3362005 3792006 4132007 4432008 4822009 526
1. What is the independent variable? Why? _______________________________________
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2. What is the dependent variable? Why? _____________________________________________________________________________________________________________________
3. What is the linear regression equation for the data? _____________________________________
4. What is your interpretation of the slope (complete sentence)? ___________________________________________________________________________________________________________________________________________________________________________________________
5. Use your prediction equation to predict how many saves Mariano Rivera will have in 2011.
6. List some of the factors that could influence the validity of your answer for question 5.
7. Write a news report consisting of at least four sentences that uses the results that you found in your investigation.
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