Question

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 x-scale from 0 to 50 in intervals of 5 and a vertical y-scale 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 x-scale from 0 to 50 in intervals of 5 and a vertical y-scale 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 x-scale from 0 to 50 in intervals of 5 and a vertical y-scale 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 x-scale from 0 to 50 in intervals of 5 and a vertical y-scale 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

Answer 1

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 R-squared value to decide which is the best model.


Choose the correct graph below: (Option B) A scatterplot has a horizontal x-scale from 0 to 50 in intervals of 5 and a vertical y-scale 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 R-squared value is the highest among all the 5 models.