# Athletic footwear is a multibillion-dollar industry, and manufacturers need to understand which features are most important to customers. The article

## Question:

Athletic footwear is a multibillion-dollar industry, and manufacturers need to understand which features are most important to customers. The article “Overall Preference of Running Shoes Can Be Predicted by Suitable Perception Factors Using a Multiple Regression Model” (Human Factors 2017: 432–441) reports a survey of 100 young male runners in Beijing and Singapore. Each participant was asked to assess the Li Ning Hyper Arc (a running shoe) on five features: y = overall preference, x_{1} = fit, x_{2 }= cushioning, x_{3} = arch support and x_{4} = stability. All measurements were made on a 0–15 visual analog scale, with 0 = dislike extremely and 15 = like extremely.

a. The estimated regression equation reported in the article is y = –.66 + .35x_{1 }+ .34x_{2 }+ .09x_{3 }+ .32x_{4}. Interpret the coefficient on x_{2}.

b. Estimate the true mean rating from runners whose ratings on fit, cushioning, arch support, and stability are 9.0, 8.7, 8.9, and 9.2, respectively. (These were the average ratings across all 100 participants.) What would be more informative than this point estimate?

c. The authors report R^{2} = .777 for this four-variable model. Perform a model utility test at the .01 significance level. Can we conclude that all four predictors provide useful information?

d. The article also reports variable utility test statistic values for each predictor; in order, they are t = 6.23, 4.92, 1.35, and 5.51. Perform all four variable utility tests at a simultaneous .01 level. Are all four predictors considered useful?

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**Related Book For**

## Modern Mathematical Statistics With Applications

**ISBN:** 9783030551551

3rd Edition

**Authors:** Jay L. Devore, Kenneth N. Berk, Matthew A. Carlton

**Question Details**

**12**- Regression and Correlation

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