The Federal Election Commission maintains data showing the voting age population, the number of registered voters,...

The Federal Election Commission maintains data showing the voting age population, the number of registered voters, and the turnout for special electons. The following table shows the voter turnout as a percentage of the voting age population in presidential elections from 1964-2000:

Year % Vote Year % Vote Year % Vote

1964 61.92 1980 52.56 1996 49.08

1968 60.84 1984 53.11 2000 51.30

1972 55.21 1988 50.11

1976 53.55 1992 55.09

6: What is the R² value?

Solutions

Expert Solution

From the given data

Year (x)	X = X-1980	Vote (Y)	X^2	Y^2	XY
1964	-16	61.92	256	3834.0864	-990.72
1968	-12	60.84	144	3701.5056	-730.08
1972	-8	55.21	64	3048.1441	-441.68
1976	-4	53.55	16	2867.6025	-214.2
1980	0	52.56	0	2762.5536	0
1984	4	53.11	16	2820.6721	212.44
1988	8	50.11	64	2511.0121	400.88
1992	12	55.09	144	3034.9081	661.08
1996	16	49.08	256	2408.8464	785.28
2000	20	51.3	400	2631.69	1026
Total:	20	542.77	1360	29621.0209	709

Ybar = 542.77/10 = 54.277

The regression equation is Y = 54.8475 - 0.28526

X	Y	Y-hat	(Y-Yhat)^2	(Y-Ybar)^2	(Ybar-Ycap)^2
-16	61.92	59.41163636	6.291888132	58.415449	26.36449059
-12	60.84	58.27060606	6.601785216	43.072969	15.94888937
-8	55.21	57.12957576	3.684771089	0.870489	8.137188453
-4	53.55	55.98854545	5.946503934	0.528529	2.929387843
0	52.56	54.84751515	5.232725568	2.948089	0.325487538
4	53.11	53.70648485	0.355794174	1.361889	0.325487538
8	50.11	52.56545455	6.029257025	17.363889	2.929387843
12	55.09	51.42442424	13.43644563	0.660969	8.137188453
16	49.08	50.28339394	1.448156973	27.008809	15.94888937
20	51.3	49.14236364	4.655394678	8.862529	26.36449059
		Total:	53.68272242	161.09361	107.4108876

R-square = 107.4108876 / 161.09361 = 0.6667

orchestra answered 1 year ago

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