Construct a scatterplot and identify the mathematical model that best fits the data shown below. Let x represent the year since 1959, with 1960 coded as
xequals=1,
1973 coded as
xequals=14,
1986 coded as
xequals=27,
and so on. Let y represent the subway fare.
Year 
1960 
1973 
1986 
1995 
2002 
2003 


Subway Fare 
0.150.15 
0.350.35 
0.900.90 
1.351.35 
1.501.50 
1.951.95 
Choose the correct graph below.
A.
05003xy
A scatterplot has a horizontal xscale from 0 to 50 in intervals of 5 and a vertical yscale from 0 to 3 in intervals of 0.5. Six plotted points loosely follow the pattern of a curve falling at an increasing rate from left to right. The approximate coordinates of the points are as follows: (1, 2); (14, 1.5); (27, 1.4); (36, 0.9); (43, 0.4); (44, 0.2).
B.
05003xy
A scatterplot has a horizontal xscale from 0 to 50 in intervals of 5 and a vertical yscale from 0 to 3 in intervals of 0.5. Six plotted points loosely follow the pattern of a curve rising at an increasing rate from left to right. The approximate coordinates of the points are as follows: (1, 0.2); (14, 0.4); (27, 0.9); (36, 1.4); (43, 1.5); (44, 2).Your answer is correct.
C.
05003xy
A scatterplot has a horizontal xscale from 0 to 50 in intervals of 5 and a vertical yscale from 0 to 3 in intervals of 0.5. Six plotted points with no visible pattern have approximate coordinates as follows: (1, 1.5); (14, 0.9); (27, 0.4); (43, 0.2); (43, 2); (44, 1.5).
D.
05003xy
A scatterplot has a horizontal xscale from 0 to 50 in intervals of 5 and a vertical yscale from 0 to 3 in intervals of 0.5. Six plotted points with no visible pattern have approximate coordinates as follows: (1, 0.9); (14, 0.4); (27, 0.2); (36, 2); (43, 1.5); (44, 1.4).
What is the equation of the best model? Select the correct choice below and fill in the answer boxes to complete your choice. Enter only nonzero values.
(Type integers or decimals rounded to three decimal places as needed.)
A.
y equals nothing plus left parenthesis nothing right parenthesis ln xy=+lnx
B.
y equals nothing x squared plus left parenthesis nothing right parenthesis x plus left parenthesis nothing right parenthesisy=x2+x+
C.
y equals nothing x Superscript nothingy=x
D.
y equals left parenthesis nothing right parenthesis nothing Superscript xy=x
E.
y equals nothing plus left parenthesis nothing right parenthesis x
We input this data set in MS Excel and use the Insert >
Scatter option to draw a scatter plot of the data which is given
below. We also use the "Add Trendline" option on this plot for
drawing different models and use the Rsquared value to decide
which is the best model.
Choose the correct graph below: (Option B) A scatterplot
has a horizontal xscale from 0 to 50 in intervals of 5 and a
vertical yscale from 0 to 3 in intervals of 0.5. Six plotted
points loosely follow the pattern of a curve rising at an
increasing rate from left to right. The approximate coordinates of
the points are as follows: (1, 0.2); (14, 0.4); (27, 0.9); (36,
1.4); (43, 1.5); (44, 2).Your answer is correct.
The best model is: y = (0.155) e^{(0.057)
x} (because its Rsquared value is the highest among
all the 5 models.
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