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	$	47,347		46.1	1
B		48,038		55.7	1
C		48,269		58.7	1
D		47,314		45.5	0
E		32,416		42.7	0
F		30,135		53.6	1
G		33,485		58.1	0
H		38,709		25.9	1
I		37,696		31.5	0

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

	. The correlation of Income and Median Age is                       .

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

	Income = + Median Age

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

For each year

in age, the income increases

on average.

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.)

	Income = + Median Age + Coastal

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.)

Predictor	t	p-value
Constant
Median Age
Coastal

Answer 1

Following is the output of regression analysis:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.15755641
R Square	0.024824022
Adjusted R Square	-0.114486832
Standard Error	7859.622066
Observations	9
ANOVA
	df	SS	MS	F	Significance F
Regression	1	11007546.37	11007546.37	0.178191588	0.685594597
Residual	7	432415613.2	61773659.03
Total	8	443423159.6
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	35699.42616	11390.54774	3.134127258	0.016514153	8765.060738	62633.79158
Median Age	100.7998195	238.7900112	0.422127454	0.685594597	-463.848832	665.4484708

1)

It seems that there is a weak linear relationship between the variable.

The correlation coeffcient is: 0.158

2)

The least square regression line is:

Income = 35699.43 + 100.80* Median Age

3.

For each year increase in age, the income increases 100.80 on average.

4.

Following is the output of multiple regression analysis:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.353633904
R Square	0.125056938
Adjusted R Square	-0.166590749
Standard Error	8041.248004
Observations	9
ANOVA
	df	SS	MS	F	Significance F
Regression	2	55453142.75	27726571.38	0.428794549	0.669791103
Residual	6	387970016.8	64661669.47
Total	8	443423159.6
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	34713.8412	11714.24511	2.963386959	0.025172212	6050.116063	63377.56634
Median Age	67.80447245	247.5284939	0.273925928	0.793327613	-537.8759316	673.4848765
Coastal	4531.144123	5465.337219	0.82906945	0.438795513	-8842.054262	17904.34251

The model is:

Income= 34713.84+67.80* MedianAge + 4531.14*Coastal

5.

Following is the table:

	Coefficients	t Stat	P-value	Significant
Intercept	34713.84	2.96	0.03	Yes
Median Age	67.8	0.27	0.79	No
Coastal	4531.14	0.83	0.44	No