Quiz: Modeling Linear and Quadratic Data and Interpreting R2

Consider the following data which shows federal minimum wage in the United States throughout history.

Year / Wage
1939 / $0.30
1945 / $0.40
1950 / $0.50
1956 / $1.00
1965 / $1.25
1967 / $1.00
1968 / $1.15
1969 / $1.30
1970 / $1.45
1971 / $1.60
1974 / $1.90
1975 / $2.00
1976 / $2.20
1977 / $2.30
1978 / $2.65
1979 / $2.90
1980 / $3.10
1981 / $3.35
1990 / $3.80
1991 / $4.25
1996 / $4.75
1997 / $5.15
2007 / $5.85
2008 / $6.55
2009 / $7.25

a.)Graph a scatter plot of Minimum Wage vs. Year in Excel and paste the graph below. Be sure to give your graph a title and label the x and y axes.

b.)Do you think that a linear model or a quadratic model is more appropriate

for the data ? Why ?

c.)Use Excel to find a linear model for the data. Report the equation of the

linear model below. Report the R2 value for this model.

d.)Use Excel to find a quadratic model for the data. Report the equation of

the quadratic model below. Report the R2 value for this model.

e.) Based on the R2 values that you found is the linear model or the quadratic

model a better model for this data?

f.) Using the better model, predict the minimum wage for the year 2015.

The table below give the average life expectancy (in years) of a person based on various years of birth.

Let x represent the number of years since 1900. (x = 10 represents the year 1910)

Year of Birth (x) / Life Expectancy (y)
0 / 47.3
10 / 50
20 / 54.1
30 / 59.7
40 / 62.9
50 / 68.2
60 / 69.7
70 / 70.8
80 / 73.7
90 / 75.4

a.)Graph a scatter plot of Life Expectancy vs. Year of Birth in Excel and

paste the graph below. Be sure to give your graph a title and label the x and y axes.

b.) Do you think that a linear model or a quadratic model is more appropriate

for the data ? Why ?

c.) Use Excel to find a linear model for the data. Report the equation of the

linear model below. Report the R2 value for this model.

d.)Based on the R2 value that you found, is the linear model a good model

for this data?

e.) Interpret the slope of the regression line.

f.)Using the model that fits the data best, predict the Life Expectancy of a person who was born in the year 2000.

3.)Find a picture online that can be modeled by a quadratic equation and paste it into

Geometer’s Sketchpad.

a.) Using the point icon, plot points along the path of the water.

b.) Edit>Select All Points

c.) Use the esc key to get back to mouse mode.

d.) Deselect the two point on the x-axis

e.) Measure> Coordinates

f.) Enter these points into the list on your graphing calculator

g.) Find the quadratic regression equation using your graphing calculator

h.) In Sketchpad: Graph > Plot New Function and then enter your regression

equation. Paste your work below.