A regional planner is studying the demographics in a region of a particular stat

Question

A regional planner is studying the demographics in a region of a particular state. She has gather the following data on nine counties:

County Median Income Median Age Coastal
a 48157 57.7 1
b 48568 60.7 1
c 46816 47.9 1
d 34876 38.4 0
e 35478 42.8 0
f 34465 35.4 0
g 35026 39.5 0
h 38599 65.6 0
j 33315 27 0

a. Is there a liner relationship between the median income and median age?
b. which variable is the "dependent" variable?
d. Include the aspect that the county is "coastal" or not in a multiple linear regression analysis using a "dummy" variable. Does it appear to be a significant influence on incomes?

Explanation / Answer

I am not very familier with multiple regression - I do not teach it regularly. But since there was no response to your question I am attempting to help you. You may want to verify the details of the answer.

a.) Yes there is a linear correlation though it is not very strong.
b.) Median Age is independent variable and Median Income is the dependent variable.
d.) Here is the regression analysis from MINITAB:

The regression equation is
Income = 29619 + 137 Age + 10640 Coastal


9 cases used, 1 cases contain missing values


Predictor Coef SE Coef T P
Constant 29619.2 0.3 90269.67 0.000
Age 136.887 0.008 18058.14 0.000
Coastal 10639.7 0.2 54546.92 0.000


S = 0.231565 R-Sq = 100.0% R-Sq(adj) = 100.0%


Analysis of Variance

Source DF SS MS F P
Regression 2 332683471 166341736 3.10211E+09 0.000
Residual Error 6 0 0
Total 8 332683472


Source DF Seq SS
Age 1 173137785
Coastal 1 159545686


Regression Analysis: Income versus Age

The regression equation is
Income = 22805 + 362 Age


9 cases used, 1 cases contain missing values


Predictor Coef SE Coef T P
Constant 22805 6255 3.65 0.008
Age 361.6 131.2 2.76 0.028


S = 4774.12 R-Sq = 52.0% R-Sq(adj) = 45.2%


Analysis of Variance

Source DF SS MS F P
Regression 1 173137785 173137785 7.60 0.028
Residual Error 7 159545686 22792241
Total 8 332683472


Unusual Observations

Obs Age Income Fit SE Fit Residual St Resid
9 65.6 38599 46525 3012 -7926 -2.14R

R denotes an observation with a large standardized residual.

Comparing resulta of two analysis we can say that the county being coastal is significant ( see R^2 value, 52 % v/s 100% !!!!)

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