Some things to Remember !!

• Modeling - the technique of producing a mathematical description or model that can be used to solve a practical problem.
• Scatter Plot - graphs of ordered pairs used to determine the type of relationship between two variables.
• Regression Line - a line of best fit on a scatter plot which approximates a relationship between the variables.

  

   
                 Weak                              Strong                       Decreasing                    Increasing

• Use Math Tools Kit to solve problems.  Save solutions on disk and hard copy .
• Feel Free to use your textbook and class notes to help complete this assignment.

Construct scatter plots for each table to determine if the data models a linear, quadratic, or exponential function.
A.

X	5	10	15	20	25	30	35	40
Y	600	400	200	100	20	0	30	120

B.

X	5	10	15	20	25	30	35	40
Y	0.20	0.25	0.40	0.70	1.0	1.7	2.8	4.5

C.

X	5	10	15	20	25	30	35	40
Y	30	25	26	20	24	22	22	20

 
 

Question 2.

Refer to the linked page and print the graphs that are presented.  Draw a line of best fit on each graph using the various regression models.  Click here.

Question 3.

As President of the Debate Team at your school, you have a variety of responsibilities and duties.  One of which includes finding the most economical way of transporting the team to the various local competitions. ( The school has given you a very limited budget so you have to spend it wisely.) It has been decided at the last Debate Team practice that the best ways to travel are by taxi or school bus.  You've done some research and found out that taxi's in the city can only carry five passengers at a time and charge a rate of $1.25/km, while the school board can provide a bus that will carry everybody at once at $3.00/km plus service charge of $45.00. (Service charge looks after the fuel and driver costs.) You now have to make a decision and present it to the team! There are 30 people on the team.

1. What are the dependent and independent variables? 
2. What equations represent these two situations?
3. Graph the two equations on the same graph
4. At what point is it the same cost to use either the taxi or bus services?
5. When should the team use only the taxi service?
6. When should the team use only the bus service
7. Prove your answers by linking the two graphs to spreadsheets.
8. What mode of transport should be used and how much will it cost to go 5 km. and 20 km.

Statistics Canada is the country's national statistical agency, with programs organized into three broad subject matter areas: demographic and social, socio-economic and economic.  Please refer to this site and find the statistical information on life expectancy at birth in Canada.(hint: try the Canadian Stats section).
 

1. Graph the male and female data on separate graphs
2. Determine line of best fit using the linear regression model for males and females.
3. What is the equation of the regression line?
4. What will the life expectancy be for both groups in the year 2020?  Do you think your answers are realistic?  Explain.

The data in the table below represents the selling price of Ford Thunderbirds based on their age.
 

1. Complete a scatter plot of the data
2. Find the linear regression equation
3. Determine the price for a 5 year old and a 10 year old Thunderbird
4. Find the exponential regression
5. Determine the price for a 5 year old and a 10 year old Thunderbird
6. Which one is the best fit?

Thanks
Mr. Mac Donald
 

"Life is good for only two things, discovering mathematics and teaching mathematics"--Siméon Poisson