A social scientist would like to analyze the relationship between educational attainment(in years of higher education) and anual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows: Salary Education 43 52 1 : 2 40 :   0 A.What is the predicted salary for an individual who completed 6 years of higher education? (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.) B:Find the sample regression equation for the model: Salary = β0 + β1Education + ε. (Round answers to 2 decimal places.)   Data  Salary Education 43 1 52 2 80 9 42 3 62 1 50 8 104 10 41 0 35 5 57 1 91 4 47 4 66 8 59 7 141 11 41 0 77 2 67 4 131 8 40 0 SUMMARY OUTPUT                                 Regression Statistics               Multiple R 0.68022955               R Square 0.462712241               Adjusted R Square 0.432862921               Standard Error 22.64942345               Observations 20                                 ANOVA                   df SS MS F Significance F       Regression 1 7952.265 7952.265113 15.50160076 0.000966       Residual 18 9233.935 512.9963826           Total 19 17186.2                                 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 41.4244373 8.097399 5.115770985 7.23128E-05 24.41243 58.43644 24.41243 58.43644069 Education 5.653536977 1.435926 3.937207228 0.000965921 2.636769 8.670305 2.636769 8.670304893                                                       RESIDUAL OUTPUT                                 Observation Predicted Salary Residuals Standard Residuals           1 47.07797428 -4.07797 -0.184981322           2 52.73151125 -0.73151 -0.033182141           3 92.3062701 -12.3063 -0.558225716           4 58.38504823 -16.385 -0.743243502           5 47.07797428 14.92203 0.676879219           6 86.65273312 -36.6527 -1.662607599           7 97.95980707 6.040193 0.273989681           8 41.4244373 -0.42444 -0.019252935           9 69.69212219 -34.6921 -1.573672168           10 47.07797428 9.922026 0.450073813           11 64.03858521 26.96141 1.222998923           12 64.03858521 -17.0386 -0.772888645           13 86.65273312 -20.6527 -0.936830302           14 80.99919614 -21.9992 -0.99790732           15 103.6133441 37.38666 1.695899132           16 41.4244373 -0.42444 -0.019252935           17 52.73151125 24.26849 1.100844886           18 64.03858521 2.961415 0.134332976           19 86.65273312 44.34727 2.011639969           20 41.4244373 -1.42444 -0.064614016

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A social scientist would like to analyze the relationship between educational attainment(in years of higher education) and anual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows:

Salary Education

43

52

1

:

2
40 :
  0

A.What is the predicted salary for an individual who completed 6 years of higher education? (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.)

B:Find the sample regression equation for the model: Salary = β0 + β1Education + ε. (Round answers to 2 decimal places.)

 

Data 

Salary Education
43 1
52 2
80 9
42 3
62 1
50 8
104 10
41 0
35 5
57 1
91 4
47 4
66 8
59 7
141 11
41 0
77 2
67 4
131 8
40 0
SUMMARY OUTPUT              
                 
Regression Statistics              
Multiple R 0.68022955              
R Square 0.462712241              
Adjusted R Square 0.432862921              
Standard Error 22.64942345              
Observations 20              
                 
ANOVA                
  df SS MS F Significance F      
Regression 1 7952.265 7952.265113 15.50160076 0.000966      
Residual 18 9233.935 512.9963826          
Total 19 17186.2            
                 
  Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 41.4244373 8.097399 5.115770985 7.23128E-05 24.41243 58.43644 24.41243 58.43644069
Education 5.653536977 1.435926 3.937207228 0.000965921 2.636769 8.670305 2.636769 8.670304893
                 
                 
                 
RESIDUAL OUTPUT              
                 
Observation Predicted Salary Residuals Standard Residuals          
1 47.07797428 -4.07797 -0.184981322          
2 52.73151125 -0.73151 -0.033182141          
3 92.3062701 -12.3063 -0.558225716          
4 58.38504823 -16.385 -0.743243502          
5 47.07797428 14.92203 0.676879219          
6 86.65273312 -36.6527 -1.662607599          
7 97.95980707 6.040193 0.273989681          
8 41.4244373 -0.42444 -0.019252935          
9 69.69212219 -34.6921 -1.573672168          
10 47.07797428 9.922026 0.450073813          
11 64.03858521 26.96141 1.222998923          
12 64.03858521 -17.0386 -0.772888645          
13 86.65273312 -20.6527 -0.936830302          
14 80.99919614 -21.9992 -0.99790732          
15 103.6133441 37.38666 1.695899132          
16 41.4244373 -0.42444 -0.019252935          
17 52.73151125 24.26849 1.100844886          
18 64.03858521 2.961415 0.134332976          
19 86.65273312 44.34727 2.011639969          
20 41.4244373 -1.42444 -0.064614016          
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