A regional planner is studying the demographics in a region of a particular stat
ID: 3361172 • Letter: A
Question
A regional planner is studying the demographics in a region of a particular state. She has gathered the following data on nine counties.
Is there a linear relationship between the median income and median age? (Round your answer to 3 decimal places.)
Use statistical software to determine the regression equation. (Round your answers to 2 decimal places.)
Interpret the value of the slope in a simple regression equation. (Round your answer to 2 decimal places.)
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? (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. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required.)
County MedianIncome Median
Age Coastal A $46,704 53.1 1 B 49,894 56.2 1 C 46,033 55.4 1 D 46,453 58.2 0 E 31,271 43.7 0 F 33,333 50.5 0 G 36,171 48.5 0 H 31,082 32.5 1 I 31,853 38.9 1
Explanation / Answer
We use Minitab to solve this question .
Is there a linear relationship between the median income and median age? (Round your answer to 3 decimal places.)
Correlation: Income., Age
Pearson correlation of Income. and Age = 0.847
P-Value = 0.004
the correlation between Age and income is 0.847
b) Which variable is the "dependent" variable
>>>>> Age is independent variable ( becuase which is not depend on income )
C) Use statistical software to determine the regression equation. (Round your answers to 2 decimal places.)
We use minitab here .
Regression Analysis: Income. versus Age
The regression equation is
Income. = 1716 + 772.0 Age
S = 4477.82 R-Sq = 71.7% R-Sq(adj) = 67.7%
Analysis of Variance
Source DF SS MS F P
Regression 1 355957398 355957398 17.75 0.004
Error 7 140356052 20050865
Total 8 496313450
Interpret the value of the slope in a simple regression equation. (Round your answer to 2 decimal places.)
Here Slope is 772.0
If Age Increases 1 year then income will increases 772
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? (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)
>>>
Regression Analysis: Income. versus Age, Coastal
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 2 456911266 228455633 34.79 0.001
Age 1 415703803 415703803 63.30 0.000
Coastal 1 100953868 100953868 15.37 0.008
Error 6 39402184 6567031
Total 8 496313450
Model Summary
S R-sq R-sq(adj) R-sq(pred)
2562.62 92.06% 89.41% 79.36%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -5814 5508 -1.06 0.332
Age 849 107 7.96 0.000 1.03
Coastal 6856 1749 3.92 0.008 1.03
Regression Equation
Income. = -5814 + 849 Age + 6856 Coastal
is the regressio equation
Yes both the variable are significant because the p-value are less than 0.05
as well as R-squuare will increases
e) Test each of the individual coefficients to see if they are significant. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required.)
Yes both variable are significant beacuse both P-values are less than 0.05
a.Is there a linear relationship between the median income and median age? (Round your answer to 3 decimal places.)
Correlation: Income., Age
Pearson correlation of Income. and Age = 0.847
P-Value = 0.004
the correlation between Age and income is 0.847
b) Which variable is the "dependent" variable
>>>>> Age is independent variable ( becuase which is not depend on income )
C) Use statistical software to determine the regression equation. (Round your answers to 2 decimal places.)
We use minitab here .
Regression Analysis: Income. versus Age
The regression equation is
Income. = 1716 + 772.0 Age
S = 4477.82 R-Sq = 71.7% R-Sq(adj) = 67.7%
Analysis of Variance
Source DF SS MS F P
Regression 1 355957398 355957398 17.75 0.004
Error 7 140356052 20050865
Total 8 496313450
Interpret the value of the slope in a simple regression equation. (Round your answer to 2 decimal places.)
Here Slope is 772.0
If Age Increases 1 year then income will increases 772
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? (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)
>>>
Regression Analysis: Income. versus Age, Coastal
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 2 456911266 228455633 34.79 0.001
Age 1 415703803 415703803 63.30 0.000
Coastal 1 100953868 100953868 15.37 0.008
Error 6 39402184 6567031
Total 8 496313450
Model Summary
S R-sq R-sq(adj) R-sq(pred)
2562.62 92.06% 89.41% 79.36%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -5814 5508 -1.06 0.332
Age 849 107 7.96 0.000 1.03
Coastal 6856 1749 3.92 0.008 1.03
Regression Equation
Income. = -5814 + 849 Age + 6856 Coastal
is the regressio equation
Yes both the variable are significant because the p-value are less than 0.05
as well as R-squuare will increases
e) Test each of the individual coefficients to see if they are significant. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required.)
Predictor T P-value Constant -1.06 0.332 Median Age 7.96 0.000 Coastal 3.92 0.008Yes both variable are significant beacuse both P-values are less than 0.05
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