Given information: Monthly Household Spending ($) Annual Household Income ($) Household Size 4016 54000 3 3159 30000 2 5100 32000 4 4742 50000 5 1864 31000 2 4070 55000 2 2731 37000 1 3348 40000 2 4764 66000 4 4110 51000 3 4208 25000 3 4219 48000 4 2477 27000 1 2514 33000 2 4214 65000 3 4965 63000 4 4412 42000 6 2448 21000 2 2995 44000 1 4171 37000 5 5678 62000 6 3623 21000 3 5301 55000 7 3020 42000 2 4828 41000 7 5573 54000 6 2583 30000 1 3866 48000 2 3586 34000 5 5037 67000 4 3605 50000 2 5345 67000 5 5370 55000 6 3890 52000 2 4705 62000 3 4157 64000 2 3579 22000 3 3890 29000 4 2972 39000 2 3121 35000 1 4183 39000 4 3730 54000 3 4127 23000 6 2921 27000 2 4603 26000 7 4273 61000 2 3067 30000 2 3074 22000 4 4820 46000 5 5149 66000 4 EXCEL (Data Analysis) output: SUMMARY OUTPUT Regression Statistics Multiple R 0.908603921 R Square 0.825561086 Adjusted R Square 0.818138154 Standard Error 398.0910071 Observations 50 ANOVA df SS MS F Significance F Regression 2 35250755.67 17625377.84 111.2176468 1.50876E-18 Residual 47 7448393.148 158476.4499 Total 49 42699148.82 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 1304.904779 197.6548431 6.601936785 3.28664E-08 907.2745236 1702.535035 Annual Household Income ($) 0.033133009 0.003967906 8.350250854 7.68206E-11 0.025150612 0.041115406 Household Size 356.2959015 33.20089044 10.73151644 3.12342E-14 289.5043251 423.0874779 Based on the multiple regression analysis output, write the estimated multiple regression equation. Show decimal places to the thousands (e.g. 3.456) (0.5’) Interpret regression coefficients b1 and b2. (1’) (1) Interpret the multiple coefficient of determination r-square. (0.5’)
Given information: Monthly Household Spending ($) Annual Household Income ($) Household Size 4016 54000 3 3159 30000 2 5100 32000 4 4742 50000 5 1864 31000 2 4070 55000 2 2731 37000 1 3348 40000 2 4764 66000 4 4110 51000 3 4208 25000 3 4219 48000 4 2477 27000 1 2514 33000 2 4214 65000 3 4965 63000 4 4412 42000 6 2448 21000 2 2995 44000 1 4171 37000 5 5678 62000 6 3623 21000 3 5301 55000 7 3020 42000 2 4828 41000 7 5573 54000 6 2583 30000 1 3866 48000 2 3586 34000 5 5037 67000 4 3605 50000 2 5345 67000 5 5370 55000 6 3890 52000 2 4705 62000 3 4157 64000 2 3579 22000 3 3890 29000 4 2972 39000 2 3121 35000 1 4183 39000 4 3730 54000 3 4127 23000 6 2921 27000 2 4603 26000 7 4273 61000 2 3067 30000 2 3074 22000 4 4820 46000 5 5149 66000 4 EXCEL (Data Analysis) output: SUMMARY OUTPUT Regression Statistics Multiple R 0.908603921 R Square 0.825561086 Adjusted R Square 0.818138154 Standard Error 398.0910071 Observations 50 ANOVA df SS MS F Significance F Regression 2 35250755.67 17625377.84 111.2176468 1.50876E-18 Residual 47 7448393.148 158476.4499 Total 49 42699148.82 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 1304.904779 197.6548431 6.601936785 3.28664E-08 907.2745236 1702.535035 Annual Household Income ($) 0.033133009 0.003967906 8.350250854 7.68206E-11 0.025150612 0.041115406 Household Size 356.2959015 33.20089044 10.73151644 3.12342E-14 289.5043251 423.0874779 Based on the multiple regression analysis output, write the estimated multiple regression equation. Show decimal places to the thousands (e.g. 3.456) (0.5’) Interpret regression coefficients b1 and b2. (1’) (1) Interpret the multiple coefficient of determination r-square. (0.5’)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.6: Regression And Median-fit Lines
Problem 17HP
Related questions
Question
Given information:
| Monthly Household Spending ($) | Annual Household Income ($) | Household Size |
| 4016 | 54000 | 3 |
| 3159 | 30000 | 2 |
| 5100 | 32000 | 4 |
| 4742 | 50000 | 5 |
| 1864 | 31000 | 2 |
| 4070 | 55000 | 2 |
| 2731 | 37000 | 1 |
| 3348 | 40000 | 2 |
| 4764 | 66000 | 4 |
| 4110 | 51000 | 3 |
| 4208 | 25000 | 3 |
| 4219 | 48000 | 4 |
| 2477 | 27000 | 1 |
| 2514 | 33000 | 2 |
| 4214 | 65000 | 3 |
| 4965 | 63000 | 4 |
| 4412 | 42000 | 6 |
| 2448 | 21000 | 2 |
| 2995 | 44000 | 1 |
| 4171 | 37000 | 5 |
| 5678 | 62000 | 6 |
| 3623 | 21000 | 3 |
| 5301 | 55000 | 7 |
| 3020 | 42000 | 2 |
| 4828 | 41000 | 7 |
| 5573 | 54000 | 6 |
| 2583 | 30000 | 1 |
| 3866 | 48000 | 2 |
| 3586 | 34000 | 5 |
| 5037 | 67000 | 4 |
| 3605 | 50000 | 2 |
| 5345 | 67000 | 5 |
| 5370 | 55000 | 6 |
| 3890 | 52000 | 2 |
| 4705 | 62000 | 3 |
| 4157 | 64000 | 2 |
| 3579 | 22000 | 3 |
| 3890 | 29000 | 4 |
| 2972 | 39000 | 2 |
| 3121 | 35000 | 1 |
| 4183 | 39000 | 4 |
| 3730 | 54000 | 3 |
| 4127 | 23000 | 6 |
| 2921 | 27000 | 2 |
| 4603 | 26000 | 7 |
| 4273 | 61000 | 2 |
| 3067 | 30000 | 2 |
| 3074 | 22000 | 4 |
| 4820 | 46000 | 5 |
| 5149 | 66000 | 4 |
EXCEL (Data Analysis) output:
| SUMMARY OUTPUT | ||||||
| Regression Statistics | ||||||
| Multiple R | 0.908603921 | |||||
| R Square | 0.825561086 | |||||
| Adjusted R Square | 0.818138154 | |||||
| Standard Error | 398.0910071 | |||||
| Observations | 50 | |||||
| ANOVA | ||||||
| df | SS | MS | F | Significance F | ||
| Regression | 2 | 35250755.67 | 17625377.84 | 111.2176468 | 1.50876E-18 | |
| Residual | 47 | 7448393.148 | 158476.4499 | |||
| Total | 49 | 42699148.82 | ||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
| Intercept | 1304.904779 | 197.6548431 | 6.601936785 | 3.28664E-08 | 907.2745236 | 1702.535035 |
| Annual Household Income ($) | 0.033133009 | 0.003967906 | 8.350250854 | 7.68206E-11 | 0.025150612 | 0.041115406 |
| Household Size |
356.2959015 | 33.20089044 | 10.73151644 | 3.12342E-14 | 289.5043251 | 423.0874779 |
- Based on the multiple regression analysis output, write the estimated multiple regression equation.
Show decimal places to the thousands (e.g. 3.456) (0.5’)
- Interpret regression coefficients b1 and b2. (1’)
- (1) Interpret the multiple coefficient of determination r-square. (0.5’)
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