Quadratic curve fitting The table shows the monthly sales (thousands) for a new hair salon since its grand opening in March
Month. 0, 1, 2, 3,. 4,. 5
Sales 5.6, 5.8, 6.2, 6.9, 7.9,. 9.0.
1) Find the best fitting quadratic model.

2) What is the prediction for total sales in September?

Algebra 1 Notes A.11 Quadratic Regression Mrs. Grieser

Name: Date: Block:

Linear Regression Review

Suppose we have the following points:

1) Draw a scatter plot of the data:

2) What is the line of best fit?

Use the calculator:

 Turn on diagnostics (Catalogue: DiagnosticsOn) to view correlation coefficient. The

closer |r| = 1, the better the data fit

 <STAT PLOT> Turn plot 1 on, and choose scatter plot, L1, L2

 Enter x values in L1

 Enter y values in L2

 <STAT><CALC><4:LinReg>L1, L2, <VARS><Y-VARS><1:Function><1:Y1> <enter>

 Y = ax + b = equation of line of best fit. Equation:

 Press <ZOOM>< 9:ZoomStat>

Questions: What would we expect the y-value to be for x value 59? 64? 67?

Use the equation or TABLE feature of the calculator to find out…

x = 59, y = , x = 64, y = , x = 67, y =

What would we expect the x-value to be for a y value of 2?

 The line of best fit allows us to make predictions for data that is almost linear.

 What if data is not linear but is more like another curve?

Algebra 1 Notes A.11 Quadratic Regression Mrs. Grieser Page 2

Quadratic Curve of Best Fit (Quadratic Regression)

 Plot the data (same as linear regression)

 Use calculator QUADREG function to find curve equation and predict values.

 Calculator regression functions: <STAT><CALC>…

o 5: QuadReg: quadratic regression – finds a quadratic of best fit (y=ax2+bx+c)

Example 1:

The table shows the monthly sales (thousands) for a new hair salon since its grand opening

in March.

Month 0 1 2 3 4 5

Sales 5.6 5.8 6.2 6.9 7.9 9.0

1) Find the best fitting quadratic model.

2) What is the prediction for total sales in September?

3) How do you know that the better model to use a quadratic fit rather than a linear fit?

Example 2:

Mrs. Grieser's class did an experiment by rolling a marble down different length slanted

boards and timing how long it took. The results are shown below:

sec. 0 4.5 11 13.4 10 8.9 14.1 9.5 12.6

cm. 0 10 60 90 50 40 100 45 80

1) Plot the data:

2) What is the quadratic curve of best fit?

3) Based on the graph, how long would it take for the

marble to roll 15 cm?

4) Approximately how far will the marble travel in 3

seconds?

5) How do we know that a quadratic model is better than a linear model for this example?