Algebra 1 A.11 Quadratic Regression WS
Mr. LUNT
Name: ________________________________________ Date: 4/______/16
Block: _________
1) For each table of data, decide if the data is a good fit for a quadratic model by finding
the coefficient of determination (R2). Explain your answer. If you think it is a good fit,
find the quadratic regression equation that fits the data.
a) R2 ________
b) R2 ________
c) R2 ________
Quadratic fit? (yes/no)
Quadratic fit? (yes/no)
Quadratic fit? (yes/no)
If yes, equation _________
If yes, equation _________
If yes, equation
_________
x
y
2
1
3
-0.9
4
-3
5
-4.9
6
-7.1
7
-9
2) A garden hose sprays a stream of water across a lawn. The table shows the approximate
height of the stream at various distances from the nozzle. Determine the equation of the
curve of best fit.
a) Plot the data.
b) Does this data better fit a linear or quadratic
regression? Use the coefficient r2 (for the linear
regression) and R2 (for the quadratic regression) to
explain.
c) Find the quadratic curve of best fit. Equation is ____________________________________
d) Use the model you found in the previous answer to determine the approximate height of
the water if you stand 2.8 m from the nozzle.
Algebra 1 A.11 Quadratic Regression WS
Mrs. Grieser Page 2
3) The table at right gives the average amount, in thousands of dollars, of an individual’s
retirement fund.
a) Find a quadratic regression model for the data. Note: use x=0 for
1985, x = 1 for 1986, etc. Find the coefficient of determination. Is
this a good fit for the data? Why?
b) To the nearest thousand dollars, what will the fund be worth in
2014?
4) The table at right gives the average cost, to the nearest hundred, of a new 4-door sedan.
a) Find a quadratic regression model for the data. Note: use x=0 for
1990. Find the coefficient of determination. Is this a good fit for
the data? Why?
b) Using this regression model, estimate during which year the
average cost of a new 4-door sedan reached approximately
$37,000.
5) Sales of a new T-shirt style are shown in the table below. These sales were recorded at
two-month intervals for one year and the values for sales, S, of the new T-shirt style are
given in thousands of dollars.
a) Write a quadratic regression model/equation for the data. Find the
coefficient of determination (R2). Is this a good fit for the data?
Why?
b) Using this regression equation, estimate, to the nearest thousand
dollars, sales for month 11 of this year.