Question

A regional planner employed by a public university is studying the demographics of nine counties in the eastern region of an Atlantic seaboard state. She has gathered the following data:

County

County	Median Income	Median Age	Coastal
A	$48,952	48.3	1
B	46,669	58.8	1
C	47,780	48.0	0
D	46,855	39.2	1
E	37,724	51.9	1
F	35,414	56.2	1
G	34,389	49.1	0
H	38,128	30.3	0
I	30,384	38.9	0

A.)Use regression analysis to determine the relationship between median income and median age. (Round your answers to 2 decimal places.)

Income=__________+_________Median Age

B.)Interpret the value of the slope in a simple regression equation. (Round your answers to 2 decimal places.)

For each year (increase/decrease) in age, the income increases ____________ on average.

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
48.3	$48,952	2.42	68104673.20	12837.31
58.8	46,669	145.34	35635593.53	71966.31
48	47,780	1.58	50134266.98	8890.03
39.2	46,855	56.92	37890864.20	-46440.25
51.9	37,724	26.58	8853269.64	-15340.07
56.2	35,414	89.41	27935922.98	-49976.81
49.1	34,389	5.55	39821709.08642	-14864.6025
30.3	38,128	270.42	6612326.53086	42285.975
38.9	30,384	61.54	106408394.09	80918.93

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	420.70	366295.00	659.74	381397020.22	90276.8
mean	46.74	40699.44	SSxx	SSyy	SSxy

a)

sample size ,   n =   9          
here, x̅ = Σx / n=   46.744   ,     ȳ = Σy/n =   40699.444  
                  
SSxx =    Σ(x-x̅)² =    659.7422          
SSxy=   Σ(x-x̅)(y-ȳ) =   90276.8          
                  
estimated slope , ß1 = SSxy/SSxx =   90276.8   /   659.742   =   136.83651
                  
intercept,   ß0 = y̅-ß1* x̄ =   34303.09787          
                  
so, regression line is   Ŷ =   34303.10   +   136.84   *x

B)

For each year (increase) in age, the income increases _____136.84_______ on average.

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