Quadratic Regression
1. Enter the data in 2 lists:
STAT
ENTER
2. Find the quadratic regression equation:
CALC
STAT
5 VARS Y­VARS ENTER
ENTER
ENTER
3. Turn the plots on:
ENTER (Plot1 should be highlighted)
Y=
3. Display the quadratic and the scatter plot:
ZOOM
9
Zoom out if necessary: ZOOM
3 ENTER as needed
To find the correlation coefficient (r2) on the calculator: Diagnostics must be turned on
1. Get to the catalog
2nd 0
2. Skip to D
X­1
3. Select DiagnosticOn
ENTER
ENTER
Find the quadratic regression model for each table. Then tell the correlation coefficient r2
Ex 1:
Ex 2:
x
­1
1
2
f(x)
­1
3
8
x
­1
1
2
f(x)
17
17
8
Ex 3: A man throws a ball off the top of a building. The table shows the height of the ball at different times.
Time (in sec) Height (in ft)
0
46
1
63
2
48
3
1
a) Find a quadratic model for the data
b) Use the model to estimate the height of the ball at 2.5 seconds.
Ex 4: The table shows the percent of US houses with cable TV
Year
1960
1970
1980
1990
2000
% of Households
0
7
20
56
68
a) Find a quadratic model using 1960 as year 0, 1970 as year 10, and so on.
b) Use the model to estimate the percent of households with cable TV in 1995
Is it linear or quadratic?
1. Find the linear and quadratic regressions for each.
2. Find the r2 for both.
3. Whichever r2 is closer to 1 is the answer.
Is it linear or quadratic?
Ex 5: Let x = 0 represent 1980.
Year
1980 1985 1990 1995 2000
Enrollment
14
20
22
28
37
Linear Equation:
Quadratic Equation:
r2:
r 2:
Is it linear or quadratic?
Ex 6:
Years after 2000
­1
0
1
2
3
4
US Student to Teacher Ratio
6
­1
­3
­1.5
5
10
Linear Equation:
r2:
Quadratic Equation:
r2: