WearRight recently released multiple models of its new wearable, the WristWrap, across a wide range of urban markets. Each model of the WristWrap tracks physical activity and monitors heart rate, among many other tracking and alert features; the key distinction across models is the battery life. For normal activity, the battery life across the different models ranges from 1 to 7 days.

Following the advice of EKA consulting, WearRight charged varying prices among battery-life models across many different markets. Table A.6 provides summary statistics for the WristWraps pricing and battery life across all models and markets. Here, Unit Sales/1,000 is wearable unit sales per 1,000 in the observed market.

WearRight wants to understand how unit sales depend on price and battery life, as well as the trade-off between these two product features. To address these issues, it asks EKA consulting to run an analysis. EKA assumes the following data-generating process for the unit sales in market i:

EKA analysts then regressed Unit Sales (per 1,000) on the Price and Battery Life; the results of this regression are in Table A.7.

1. Describe the results in Table A.6.

   1. Is variation in Price for each model across markets important? If so, why?

   2. Suppose instead that WearRight simply charged $10 more for each 1-day increase in battery life in every market. How would that affect the regression results in Table A.7?

2. Explain the results for Battery Life in Table A.7.

   1. What does the point estimate mean?

   2. What does the p-value mean?

   3. What do the upper and lower bounds for the 95% confidence interval mean?

3. Explain the results for the Price in Table A.7.

   1. What does the point estimate mean?

   2. What does the p-value mean?

   3. What do the upper and lower bounds for the 95% confidence interval mean?

4. Predict the effect of raising the Battery Life by 1 day on Unit Sales per 1,000.

5. Detail the line of reasoning necessary to make your prediction in Question 4.

6. On average, how much is an extra day of Battery life worth? (hint: determine how much the price could increase along with a 1-day increase in Battery Life without reducing Unit Sales per 1,000).

7. Suppose WearRight is concerned that there are inherent differences in market performance for the WristWrap, and the price/battery life combinations offered across markets are determined at least in part based on those differences.

   1. How would this data feature damage the line of reasoning you presented in Question 5?

   2. How might you append the data and the assumed data-generating process to remedy this problem?