Question

Exercise 14-22 (LO14-1, LO14-5)

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	$	49,374		58.5	0
B		46,850		46.5	1
C		47,586		48.5	1
D		47,781		45.5	1
E		33,738		37.3	0
F		35,553		43.4	0
G		39,910		45.3	0
H		37,266		34.2	0
I		34,571		36.5	0

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

   Yes. The correlation of Income and Median Age is

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

   1. Income =

      +

      Median Age

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

For each year increases in age, the income increases

on average

C. 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.)

1. Income =

   +

   Median Age +

   Coastal

D.

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

(A) Correlation between INCOME and AGE is given by,

where COV is the covariance between Income and Age, and SD is the standard deviation of Income and Age.

(B) To fit the regression line on Income vs Age.

Therefore, Income = 10171 + 710.36 Age

(C) For each year increase in age, the income increases by 710.36 dollars on average.

(D) For MLR, we use R for computing the regression coefficients. We can use lm(INCOME~AGE+COASTAL) command to obtain the results. I will attach the R code in the end of the answer. We are using R, otherwise the computations will be very lengthy and complex.

The fitted model is, Income = 13611.4 + 582.9 Age + 6497.4 Coastal

(E)

Predictor	t value	p value
constant	2.698	0.035
age	5.003	0.002
coastal	3.768	0.009

###########################################

R CODE

###########################################

rm(list=ls(all=TRUE))

INCOME=c(49374,46850,47586,47781,33738,35553,39910,37266,34571)
AGE=c(58.5,46.5,48.5,45.5,37.3,43.4,45.3,34.2,36.5)
COASTAL=c(0,1,1,1,0,0,0,0,0)

summary(lm(INCOME~AGE))

summary(lm(INCOME~AGE+COASTAL))