To find the line of Best Fit on the calculator you must do ...



LINE of BEST FIT Common Core Math 1

Example 1: 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.

a)

|Year |Cost of Stamp |

|1958 |0.04 |

|1963 |0.05 |

|1968 |0.06 |

|1971 |0.08 |

|1974 |0.10 |

|1975 |0.13 |

|1978 |0.15 |

|1981 |0.18 |

|1985 |0.22 |

|1988 |0.25 |

|1991 |0.29 |

|1995 |0.32 |

i. Equation of line of Best Fit:_______________

ii. Predict cost of stamp in 2000:_____________

iii. Slope represents:______________________

iv. y-intercept represents:__________________

b)

|Weight(tons) |Miles Per Gallon |

|1.3 |29 |

|1.4 |24 |

|1.5 |23 |

|1.8 |21 |

|2.1 |17 |

|2.4 |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:__________________

c)

|Year |Trash (millions of tons) |

|1960 |88 |

|1965 |103 |

|1970 |122 |

|1975 |128 |

|1980 |152 |

|1985 |164 |

|1990 |196 |

i. Equation of line of Best Fit:_______________

ii. Predict Trash in 2010:___________________

iii. Slope represents:______________________

iv. y-intercept represents:__________________

d)

|Length |Weight (long tons) |

|40 |25 |

|42 |29 |

|45 |34 |

|46 |35 |

|50 |43 |

|52 |45 |

|55 |51 |

i. Equation of line of Best Fit:_______________

ii. Predict weight for a length of 60:__________

iii. Slope represents:______________________

iv. y-intercept represents:__________________

NEWS 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 Illness |

|8/29/09 |34 |420 |

|9/5/09 |35 |1635 |

|9/12/09 |36 |2786 |

|9/19/09 |17 |4187 |

|9/26/09 |38 |5506 |

|10/3/09 |39 |6662 |

|10/10/09 |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.) Let 1990 = 0

|Year |Career Saves |

|1995 |0 |

|1996 |5 |

|1997 |48 |

|1998 |84 |

|1999 |129 |

|2000 |165 |

|2001 |215 |

|2002 |243 |

|2003 |283 |

|2004 |336 |

|2005 |379 |

|2006 |413 |

|2007 |443 |

|2008 |482 |

|2009 |426 |

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. 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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LINE OF BEST FIT Common Core Math 1

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 Shakeel 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 99cents. A double hamburger cost $1.49. Assuming this relationship is linear, predict the cost of a triple hamburger.

A) What is the slope of this line?

6. Graph f(x) = 2x -3 Graph 3x – y = 4

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Data Analysis: Line of Best Fit Name:_______________________________

For each of the following, write the prediction equation and then solve the problem.

1. A student who waits on tables at a restaurant recorded the cost of meals and the tip left by single diners.

|Meal Cost |$4.75 |$6.84 |$12.52 |$20.42 |$8.97 |

|Tip |$0.50 |$0.90 |$1.50 |$3.00 |$1.00 |

If the next diner orders a meal costing $10.50, how much tip should the waiter expect to receive?

Equation______________________________________ Tip Expected___________________

Slope represents______________________________________________________________________

Y-intercept represents___________________________________________________________________

2. The table below give the number of hours spent studying for a science exam (x) and the final exam grade (y).

|X |2 |5 |1 |0 |4 |2 |3 |

|Y |77 |92 |70 |63 |90 |75 |84 |

Predict the exam grade of a student who studied for 6 hours.

Equation______________________________________ Grade Expected___________________

Slope represents______________________________________________________________________

Y-intercept represents___________________________________________________________________

3. The table below shows the lengths and corresponding ideal weights of sand sharks.

|Length |60 |62 |64 |66 |68 |70 |72 |

|Weight |105 |114 |124 |131 |139 |149 |158 |

Predict the weight of a sand shark whose length is 75 inches.

Equation______________________________________ Weight Expected___________________

Slope represents______________________________________________________________________

Y-intercept represents___________________________________________________________________

4. The table below gives the height and shoe size of six randomly selected men.

|Height |67 |70 |73.5 |75 |78 |66 |

|Shoe Size |8.5 |9.5 |11 |12 |13 |8 |

If a man has a shoe size of 10.5, what would be his predicted height?

Equation______________________________________ Height Expected___________________

Slope represents______________________________________________________________________

Y-intercept represents___________________________________________________________________

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