Question

In: Statistics and Probability

The data below lists the population of the United States each year from 2000 until 2010....

The data below lists the population of the United States each year from 2000 until 2010. (Hint: see Chapter 7 Project Part 1) a. (4 points) Use EXCEL to make a scatter plot and find a linear model of your data. Let the horizontal axis represent the years after 2000 (the year 2000 would be 0) and let the vertical axis represent the US population in millions. Provide a title for your graph, label both the vertical and horizontal axes, and make sure the linear model is included on your graph. Copy the scatter plot with the linear model and paste it into your document. b. (3 points) Identify the slope and y-intercept of your linear model and explain what both of these values mean in the context of the data given labeling with correct units. Please use complete sentences. (hint: see last page of part 1 of the project). Year US Population in Millions 2000 282.16 2001 284.97 2002 287.62 2003 290.11 2004 292.81 2005 295.52 2006 298.38 2007 301.23 2008 304.09 2009 306.77 2010 309.3

Expert Solution

Year	US Population(In Millions)
2000	282.16
2001	284.97
2002	287.62
2003	290.11
2004	292.81
2005	295.52
2006	298.38
2007	301.23
2008	304.09
2009	306.77
2010	309.3

Estimation Method in Excel (Manual as well as by using formula)

Linear Model
y=aX+b

a	b
2.728364	-5174.645455
Formula Used
= Linest([y value range],[x value range])

(Make sure to select two cells to use this formula and press ctrl+shift+ Enter to execute the formula)

Manual Method

The independent variable is YearsYears, and the dependent variable is US PopulationUSPopulation. In order to compute the regression coefficients, the following table needs to be used:

	Years	US Population	Years*US Population	Years²	US Population²
	2000	282.16	564320	4000000	79614.2656
	2001	284.97	570224.97	4004001	81207.9009
	2002	287.62	575815.24	4008004	82725.2644
	2003	290.11	581090.33	4012009	84163.8121
	2004	292.81	586791.24	4016016	85737.6961
	2005	295.52	592517.6	4020025	87332.0704
	2006	298.38	598550.28	4024036	89030.6244
	2007	301.23	604568.61	4028049	90739.5129
	2008	304.09	610612.72	4032064	92470.7281
	2009	306.77	616300.93	4036081	94107.8329
	2010	309.3	621693	4040100	95666.49
Sum =	22055	3252.96	6522484.92	44220385	962796.1978

Based on the above table, the following is calculated:(in excel)

Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows:

US Population(in Millions) = −5174.6455 + 2.7284*(Years)

Interpretation

For Slope

When there is increase in one year(X value) then there is 2.7284 times increase in the US population(in millions).

For intercept

The intercept (often labeled the constant) is the expected mean value of Y when all X=0.

Here intercept values is negative which do not have physical Interpretation in this context but it says that when year is 0 the population values is negative 5174.6455 (in millions).

orchestra answered 2 years ago

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