question archive Designers of backpacks use exotic material such as supernylon Delrin, high-density ethylene, aircraft aluminum, and thermo molded floam to make packs that fit comfortably and distribute weight to eliminate pressure points
Designers of backpacks use exotic material such as supernylon Delrin, high-density ethylene, aircraft aluminum, and thermo molded floam to make packs that fit comfortably and distribute weight to eliminate pressure points
Subject:StatisticsPrice:2.87 Bought7
Designers of backpacks use exotic material such as supernylon Delrin, high-density ethylene, aircraft aluminum, and thermo molded floam to make packs that fit comfortably and distribute weight to eliminate pressure points. The following data show the capacity (cubic inches), comfort rating, and price (dollars) for 10 backpacks tested by Outside Magazine. Comfort was measured using a rating from 1 to 5, with a rating of 1 denoting average comfort and a rating of 5 denoting excellent comfort. Regress price on comfort and capacity using excel and answer the following questions.
please show how to solve with answers
| What is the interpretation of adjusted R-square for this problem? | ||||||||||
| What price would you predict for a backpack with a mean capacity of 5700 (cubic inches) and comfort rating of 4? | ||||||||||
| Manufacturer & Model | Capacity | Comfort | Price ($) | ||
| Camp Trails Paragon | 4330 | 2 | 190 | ||
| EMS 5500 | 5500 | 3 | 219 | ||
| Lowe Almayo | 5500 | 4 | 249 | ||
| Marmot Muir | 4700 | 3 | 249 | ||
| Kelly Bigfoot | 5200 | 4 | 250 | ||
| Gregory Whitney | 5500 | 4 | 340 | ||
| Osprey 75 | 4700 | 4 | 389 | ||
| Arc' Teryx Bora | 5500 | 5 | 395 | ||
| Dana Design Terraplane | 5800 | 5 | 439 | ||
| The Works @ Mystery | 5000 | 5 | 525 |
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Answer:
In case of any clarity problems, I have also pasted the output from Excel
| SUMMARY OUTPUT | ||||||||
| Regression Statistics | ||||||||
| Multiple R | 0.912054 | |||||||
| R Square | 0.831842 | |||||||
| Adjusted R Square | 0.783797 | |||||||
| Standard Error | 51.13629 | |||||||
| Observations | 10 | |||||||
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 2 | 90548.06 | 45274.03 | 17.31373 | 0.00195 | |||
| Residual | 7 | 18304.44 | 2614.921 | |||||
| Total | 9 | 108852.5 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | 356.1208 | 197.174 | 1.806125 | 0.113859 | -110.122 | 822.3633 | -110.122 | 822.3633 |
| X Variable 1 | -0.09874 | 0.045877 | -2.15239 | 0.068372 | -0.20722 | 0.009737 | -0.20722 | 0.009737 |
| X Variable 2 | 122.8672 | 21.79975 | 5.636175 | 0.000786 | 71.31899 | 174.4154 | 71.31899 | 174.4154 |
The adjusted R2 for this problem is 0.7838. It means that the regression model explains 78.38% of the variation in the data.
From the output, the regression equation becomes Price = 356.1208 - 0.0987(Capacity) + 122.8672 (Comfort)
When capacity = 5700 and comfort = 4, Price = 356.1208 - 0.0987(5700) + 122.8672(4) = 284.9996 which is approximately 285 $.
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