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	Median Income			Median Age	Coastal
A	$	47,963		56.4	1
B		49,585		58.9	1
C		46,440		57.5	1
D		46,391		41.2	1
E		34,806		39.4	0
F		39,416		41.2	1
G		35,549		41.3	0
H		30,796		33.5	0
I		32,233		21.7	1

  Click here for the Excel Data File

1. Is there a linear relationship between the median income and median age? (Round your answer to 3 decimal places.)

2. Which variable is the "dependent" variable?

• Median Age

• Median Income

1. c-1. Use regression analysis to determine the relationship between median income and median age. (Round your answers to 2 decimal places.)

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

4. Include the aspect that the county is "coastal" or not in a multiple linear regression analysis using a "dummy" variable. (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)

5. Test each of the individual coefficients to see if they are significant. (Negative amounts should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 2 decimal places.)

Answer 1

using excel>data>data analysis>Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.861572
R Square	0.742306
Adjusted R Square	0.705492
Standard Error	3972.402
Observations	9
ANOVA
	df	SS	MS	F	Significance F
Regression	1	3.18E+08	3.18E+08	20.16399	0.002831
Residual	7	1.1E+08	15779978
Total	8	4.29E+08
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	18041.7	5142.09	3.508632	0.009878	5882.593	30200.82
Median Age	513.433	114.3393	4.490433	0.002831	243.0635	783.8025

a)yes there a linear relationship between the median income and median age because the value of correlation coefficient is 0.862

b )Which variable is the "dependent" variable?

• Median Income

c-1. Use regression analysis to determine the relationship between median income and median age.

median income = 18041.7+513.433 *median age

c-2. Interpret the value of the slope in a simple regression equation.

for every one year increase in median age , there is corresponding $513.433 increase in income

using excel>data>data analysis>Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.95842
R Square	0.918569
Adjusted R Square	0.891426
Standard Error	2411.949
Observations	9
ANOVA
	df	SS	MS	F	Significance F
Regression	2	3.94E+08	1.97E+08	33.84119	0.00054
Residual	6	34904997	5817499
Total	8	4.29E+08
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	17490.87	3125.896	5.595474	0.001387	9842.077	25139.66
Median Age	426.2556	73.5179	5.797984	0.001154	246.3638	606.1475
Coastal	6508.767	1806.075	3.603819	0.011315	2089.461	10928.07

d )Include the aspect that the county is "coastal" or not in a multiple linear regression analysis using a "dummy" variable.

median income = 17490.87+426.26 *Median Age+ 6508.77*Coastal

e ) Test each of the individual coefficients to see if they are significant.

			t Stat	P-value
Intercept			5.60	0.00
Median Age			5.80	0.00
Coastal			3.60	0.01

median age and coastal is significant variableTest each of the individual coefficients to see if they are significant.