Simple Regression

Use the following scenario as the basis for this discussion:

Imagine that you own a faucet factory. You know that every so often you produce a faucet that is defective. You know this because retailers send them back to you and you have to refund the value of the faucet plus shipping, and then you have to fix the faucet or trash it. Fixing it costs you money, and trashing it costs the most because you have a lot of money tied up in a faucet that you are throwing away.

You have a working hypothesis that if you inspect some faucets coming off the production line, you will find some defective ones and fix them right away, which is a cheaper alternative to shipping them to customers and then needing to refund money.

You could test this hypothesis with a bivariate correlation by having inspectors examine different numbers of faucets and correlating that with the number of defective faucets found. But, even if you found a significant positive correlation here, that would not be enough information to help you lean your quality assurance process within some specification. Simple regression would be better because it gives you more information. Why is that the case?

What you really want to know is: How many faucets should inspectors examine to reduce the number of defective faucets reaching customers to 100 per 10,000 faucets?

Your variables are the number of faucets inspected and the number of faucets found to be defective.

Based on this scenario, answer the following:

Identify the independent and dependent variables in this research question.

Identify the level of measurement of each variable.

Determine whether the appropriate design would assess a causal or correlational relationship between the independent and dependent variable.

Identify which statistical technique would be most appropriate for this research question.

Identify the assumptions of the statistical technique.

Identify the tests you would use to examine the assumptions.

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Use the following scenario as the basis for this discussion:

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