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
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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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