(New questions I promise.) Designers of backpacks use exotic material such as su

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(New questions I promise.) 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.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.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.

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

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?

Provide the appropriate test statistic and p-value for assessing whether there is evidence that Comfort aids in predicting Price.

  test statistic ---->

  p-value ----->

Provide an interpretation for the sample regression coefficient of capacity.

  Sample regression coefficient ---->

  Interpretation -->

Is the overall model significant at 0.05 level of significance? Why or Why not.

Does Capacity aid in predicting price at 0.05 level of significance? Why or Why not.

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

Explanation / Answer

Below is result from multiple regression from Excel

What is the interpretation of adjusted R-square for this problem?

adjusted R-square = 0.78379

this model explains 78.38 % of the variation

What price would you predict for a backpack with a mean capacity of 5700 (cubic inches) and comfort rating of 4?

price^ = 356.1208 -0.0987*capacity + 122.8672 *comfort

= 356.1208 -0.0987*5700 + 122.8672 *4

= 284.9996

Provide the appropriate test statistic and p-value for assessing whether there is evidence that Comfort aids in predicting Price.

  test statistic ----> 5.6361

  p-value -----> 0.000785

Provide an interpretation for the sample regression coefficient of capacity.

  Sample regression coefficient ----> -0.0987544

  Interpretation --> if capacity is increased bu 1 unit , the price will decrease by -0.0987444 unit

Is the overall model significant at 0.05 level of significance? Why or Why not.

significance F = 0.00195 < 0.05

hence the model is significant

Does Capacity aid in predicting price at 0.05 level of significance? Why or Why not.

if p-value < 0.05 ,the variable is significant

for capacity , p-value = 0.068 > 0.05 , hence insignificant

for comfort , p-value = 0.00078 < 0.05 , hence significant

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if some part is not clear or you would like to be elaborated upon. Thanks and have a good day!

SUMMARY OUTPUT Regression Statistics Multiple R 0.912053596 R Square 0.831841762 Adjusted R Square 0.783796551 Standard Error 51.13629498 Observations 10 ANOVA df SS MS F Significance F Regression 2 90548.05535 45274.02768 17.31372898 0.001949905 Residual 7 18304.44465 2614.920664 Total 9 108852.5 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 356.1208346 197.1740072 1.806124649 0.113859073 -110.1216047 822.3632739 Capacity -0.098744049 0.045876543 -2.15238646 0.068372269 -0.207224835 0.009736736 Comfort 122.8672136 21.79975287 5.63617461 0.000785707 71.31898931 174.4154379

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