A regional planner employed by a public university is studying the demographics

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:

  Click here for the Excel Data File

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

Which variable is the "dependent" variable?

Median Age

Median Income

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

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

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.)

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.)

Make a histogram of the residuals. Which plot is correct?

Plot 1

Plot 2

Plot 3

Make a scatter diagram of the residual values versus the fitted values. Which plot is correct?

County Median Income Median Age Coastal A $ 48,821 58.9 0 B 46,412 54.5 0 C 46,371 46.8 1 D 47,115 49.5 1 E 33,949 35.8 1 F 39,429 38.5 1 G 34,438 38.4 0 H 37,191 37.5 1 I 36,863 35.5 1

Explanation / Answer

i am answering 4 parts as per company policies

A)

Corr coef, r =
{n*sum(XY)-sum(X)*sum(Y)}/{ sqrt(n*sum(x^2)-[sum(x)]^2) * sqrt(n*sum(y^2)-[sum(y)]^2) }
{9*16666475.1-395.4*370589}/{ sqrt(9*17984.9-[395.4]^2) * sqrt(9*15542864387-[370589]^2) }
0.924

B)

Dependent variable: Median Income

C1)

Slope, b1=
{n*sum(xy)-sum(x)*sum(y)}/{n*sum(x^2)-[sum(x)]^2 }
{9*16666475.1-395.4*370589}/{9*17984.9-[395.4]^2 }
627.8151

Intercept, bo=
{sum(y)*sum(x^2)-sum(x)*sum(xy)}/{n*sum(X^2)-[sum(X)]^2}
{370589*17984.9-395.4*16666475.1}/{9*17984.9-[395.4]^2}
13594.5441

Regression equation:
y = bo + b1*x
y = 13594.54 + 627.82*x

C2)with one unit increase in median age, there is 627.82 units increase in median income.

Median Income Median Age X^2 Y^2 Xy 58.9 48,821 3469 2383490041 2875557 54.5 46,412 2970 2154073744 2529454 46.8 46,371 2190 2150269641 2170163 49.5 47,115 2450 2219823225 2332193 35.8 33,949 1282 1152534601 1215374 38.5 39,429 1482 1554646041 1518017 38.4 34,438 1475 1185975844 1322419 37.5 37,191 1406 1383170481 1394663 35.5 36,863 1260 1358880769 1308637

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