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 $ 48,725 55.3 1
B 48,383 53.7 1
C 46,862 46.5 1
D 48,777 57.9 0
E 36,339 43.4 0
F 37,618 40.3 0
G 37,495 37.2 0
H 38,301 31.2 1
I 37,705 32.5 1

(a) Is there a linear relationship between the median income and median age? (Round your answer to 3 decimal places.) What is the Correlation?
(b) Which variable is the "dependent" variable?
(c) Use regression analysis to determine the relationship between median income and median age. (Round your answers to 2 decimal places.)
(d) Interpret the value of the slope in a simple regression equation. (Round your answers to 2 decimal places.)

Answer 1

Answer:

Step-by-step explanation:

Hello!

Given the variables:

X₁: Median Age

X₂: Median Income

b) Considering it from a logical point of view, income changes with age, for example, the more experienced the worker is you would think he would get a better paying job than a younger worker who is just starting. Then the dependent variable will be the median income and the independent variable will be the median age.

a)  and c)

To see if there is a linear regression between the median income and median age you have to conduct a hypothesis test for the slope. If the slope is equal to zero, there is no linear regression between the two variables, if it is different to zero, there is a regression between the two of them:

H₀: β=0

H₁: β≠0

α: 0.05

$t= \frac{b-\beta }{Sb} ~~t_{n-2}$

The estimated regression equation for this regression ^Yi= 20.01 + 0.50X

The standard deviation for the slope is Sb= 0.11

$t_{H_0}= \frac{0.50-0}{0.11} = 4.545$

And the p-value for the test is 0.0022

The p-value is less than the level of significance I choose, so the decision is to reject the null hypothesis. You can conclude that there is a linear regression between these two variables.

The correlation coefficient between the median income and the median age is r= 0.87 ⇒ This means you could expect a positive and strong linear correlation between the two variables.

d)

The slope represents how much the variable Y is modified whenever the variable X increases one unit.

In this example: Is the modification of the population mean of the median income, when the median age increases one year.