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) 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 _______

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

Income=__________+_________Median Age

C.)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.

D.)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

E.)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

using minitab>stat>basic stat>correlation

we have

Correlation: median income, median age

Pearson correlation of median income and median age = 0.180
P-Value = 0.643
a ) The correlation of income and Median age is 0.180

using minitab>stat>Regression >line plot

we have

Regression Analysis: median income versus median age

The regression equation is
b ) median income = 34303 + 136.80 median age

c ) For each year increase in age, the income increases 136.80 on average..

d ) using minitab>stat>Regression

we have

Regression Analysis: median income versus median age, coastal

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 2 67147699 33573850 0.64 0.559
median age 1 1080362 1080362 0.02 0.891
coastal 1 54794534 54794534 1.05 0.346
Error 6 314249321 52374887
Total 8 381397020

Model Summary

S R-sq R-sq(adj) R-sq(pred)
7237.05 17.61% 0.00% 0.00%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 39669 14381 2.76 0.033
median age -48 335 -0.14 0.891 1.41
coastal 5900 5768 1.02 0.346 1.41

Regression Equation

median income = 39669 - 48 median age + 5900 coastal
E )

Predictor	t	p value
Constant	2.76	0.033
Median Age	-0.14	0.891
coastal	1.02

      
p value for coastal is 0.346