The value y (in 1982–1984 dollars) of each dollar paid by consumers in each of the years from 1994 through 2008 in a country is represented by the ordered pairs. (1994, 0.677) (1995, 0.655) (1996, 0.639) (1997, 0.618) (1998, 0.609) (1999, 0.605) (2000, 0.580) (2001, 0.565) (2002, 0.557) (2003, 0.542) (2004, 0.531) (2005, 0.516) (2006, 0.499) (2007, 0.478) (2008, 0.461) (a) Use a spreadsheet software program to generate a scatter plot of the data. Let t = 4 represent 1994. Do the data appear linear? Yes or No (b) Use the regression feature of the spreadsheet software program to find a linear model for the data. (Let t represent time. Round your numerical values to four decimal places.) y = (c) Use the model to predict the value (in 1982–1984 dollars) of 1 dollar paid by consumers in 2010 and in 2013. (Round your answers to two decimal places.) 2010 $ 2013 $ Discuss the reliability of your predictions based on your scatter plot and the graph of your linear model for the data.(Choose one below) Because the data follow a linear pattern, the predictions for 2010 and 2013 are reliable. Because the data does not follow a linear pattern, the predictions for 2010 and 2013 are reliable. Because the data does not follow a linear pattern, the predictions for 2010 and 2013 are not reliable. Because the data follow a linear pattern, the predictions for 2010 and 2013 are not reliable.
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
The value y (in 1982–1984 dollars) of each dollar paid by consumers in each of the years from 1994 through 2008 in a country is represented by the ordered pairs.
| (1994, 0.677) | (1995, 0.655) |
| (1996, 0.639) | (1997, 0.618) |
| (1998, 0.609) | (1999, 0.605) |
| (2000, 0.580) | (2001, 0.565) |
| (2002, 0.557) | (2003, 0.542) |
| (2004, 0.531) | (2005, 0.516) |
| (2006, 0.499) | (2007, 0.478) |
| (2008, 0.461) |
(b) Use the regression feature of the spreadsheet software program to find a linear model for the data. (Let t represent time. Round your numerical values to four decimal places.)
| 2010 | $ |
| 2013 | $ |
Discuss the reliability of your predictions based on your scatter plot and the graph of your linear model for the data.(Choose one below)
- Because the data follow a linear pattern, the predictions for 2010 and 2013 are reliable.
- Because the data does not follow a linear pattern, the predictions for 2010 and 2013 are reliable.
- Because the data does not follow a linear pattern, the predictions for 2010 and 2013 are not reliable.
- Because the data follow a linear pattern, the predictions for 2010 and 2013 are not reliable.
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