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 $ 47,347 46.1 1
B 48,038 55.7 1
C 48,269 58.7 1
D 47,314 45.5 0
E 32,416 42.7 0
F 30,135 53.6 1
G 33,485 58.1 0
H 38,709 25.9 1
I 37,696 31.5 0
Click here for the Excel Data File
a. Is there a linear relationship between the median income and median age? (Round your answer to 3 decimal places.)
b. Which variable is the "dependent" variable?
multiple choice 1
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 answer to 2 decimal places.)
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.)
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.)
f. Make a histogram of the residuals. Which plot is correct?
Residual plot 1 Residual plot 2 Residual plot 3
3 Histograms with a normal bell curve each. Plot 1 is titled Residual plot, Normal. The vertical axis plots Frequency ranging from 0.0 to 3.0 in increments of 0.5. The horizontal axis plots Residual ranging from -4000 to 4000 in increments of 2000. The values are as follow: (-3000, 1.0), (-2000, 1.0), (-1000, 1.0), (0, 3.0), (1000, 1.0), (2000, 1.0), (4000, 1.0). All values approximated. 3 given values are: Mean = 4.04E-12, StDev = 2021, N = 9. 3 Histograms with a normal bell curve each. Plot 2 is titled Residual plot, Normal. The vertical axis plots Frequency ranging from 0.0 to 2.0 in increments of 0.5. The horizontal axis plots Residual ranging from -15000 to 15000 in increments of 5000. The values are as follow: (-7500, 2.0), (-5000, 1.0), (-2500, 1.0), (0, 1.0), (2500, 1.0), (5000, 2.0), (10000, 1.0). All values approximated. 3 given values are: Mean = -8.08E-13, StDev = 6267, N = 9. 3 Histograms with a normal bell curve each. Plot 3 is titled Residual plot, Normal. The vertical axis plots frequency ranging from 0.0 to 2.0 in increments of 0.5. The horizontal axis plots Residual ranging from -12000 to 12000 in increments of 4000. The values are as follow: (-8000, 1.0), (-4000, 2.0), (2000, 1.0), (4000, 2.0), (6000, 2.0). All values approximated. 3 given values are: Mean = 1.45E-11, StDev = 5781, N = 9.
multiple choice 2
Plot 1
Plot 2
Plot 3
g. Make a scatter diagram of the residual values versus the fitted values. Which plot is correct?
Residuals vs Fits 1 Residuals vs Fits 2 Residuals vs Fits 3
3 scatter plots, Plot 1, Plot 2, Plot 3. Plot 1 is titled Residuals versus Fits for LCD's. The vertical axis plots the residual value ranging from -4000 to 4000 in increments of 1000. The horizontal axis plots fits ranging from 35000 to 50000 in increments of 2500. The data is scattered with more data having residual values under 0. 3 scatter plots, Plot 1, Plot 2, Plot 3. Plot 2 is titled Residuals versus Fits for LCD's. The vertical axis plots the residual value ranging from -10000 to 5000 in increments of 2500. The horizontal axis plots fits ranging from 35000 to 45000 in increments of 2500. The data is scattered in a random distribution. 3 scatter plots, Plot 1, Plot 2, Plot 3. Plot 3 is titled Residuals versus Fits for LCD's. The vertical axis plots the residual value ranging from -10000 to 10000 in increments of 5000. The horizontal axis plots fits ranging from 37000 to 44000 in increments of 1000. The data is scattered with data being lesser than the fits value 39000or greater than 42000.
multiple choice 3
Plot 1
Plot 2
Plot 3