# Sales per capita, advertising expenditure per capita, and average local income

Part 1 The data in the file attached contains information on your firm’s sales per capita, advertising expenditure per capita, and average local income.

Regress sales per capita on advertising expenditure per capita, controlling for local income as an interval variable, where intervals are <\$35,000, \$35,000–\$44,999, \$45,000–\$54,999, and \$55,000+, and <\$35,000 is the base group.

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For the remainder of the question, assume the data-generating process is

SalesperCapitai = α + β1AdExpperCapita+ β2Inc35-45+ β3Inc45-55i + β4Inc55i + Ui and that all other necessary assumptions toward establishing causality and performing inference hold.

1. Interpret the coefficients for the income intervals from your regression.
2. According to this regression, what is the effect on sales per capita when average local income increases from \$35,000−\$44,999 to \$55,000+?

Part 2 – To help make decisions about advertising potential for your website, you are interested in learning the average amount of time visitors to your website spend on the site. You manage to collect a month’s worth of data that includes 9,872 website visits and their duration. The data are in attached.

1. Build a 90% confidence interval for the mean visit duration for all visitors to your website. Explain what this confidence interval means.
2. Build a 95% confidence interval for the mean visit duration for all visitors to your website. Explain what this confidence interval means.
3. Build a 99% confidence interval for the mean visit duration for all visitors to your website. Explain what this confidence interval means.
4. Is there reason to believe your confidence levels are inaccurate? If so, what assumption(s) may be inaccurate?