If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Worked example of linear regression using transformed data

Worked example of linear regression using transformed data. Adapted from 2007 AP Statistics free response, form b, question 6, part d.

## Want to join the conversation?

• Why don't we take the ln(3 *15)?
• I think you mean "why don't we take the ln(3*5), right? Meaning, "why don't we use the total area of the islands, instead of the area of just one of them," right? The line Sal calculates gives the proportion of animals to go extinct versus CONTIGUOUS area (i.e. area all together in one piece). Note that the regression line has a negative slope, so the smaller the piece of land, the bigger the proportion of animals that go extinct. So, to get an accurate proportion for each of the five smaller parcels, the area for just one must be used to calculate the proportion for that one. Then the proportion for each would be multiplied times the number of animals on that one. Since they're all are the same size, and since they all have the same number of animals, once the proportion is calculated for one, using the area for just that one, or 3 sq. km, then the total predicted extinctions for the group can be calculated by just multiplying by 5. So, 5*[16*(0.28996 - 0.05323*ln(3))] would be the correct calculation.
• The conclusion reached is backwards. It is question of what is the original data saying. If the regression showed a relationship between large PRESERVED islands and small PRESERVED islands then the conclusion would make sense. However, what it appears to be asking is whether one large or five small islands should be preserved given the proportion of extinct species that has been observed on UNPRESERVED islands of various sizes. The correct answer is to preserve the 5 small islands, thereby preserving 19 total species that would have otherwise become extinct.
• The conservation group believes that all at-risk species will disappear once their habitat gets developed, so obviously the data shown must have been gathered from undeveloped lands.
• Why is it ln for natural log and not nl? It just confuses me.
• shouldn't be ln(15) be used? (that is 3 times 5, there were 5 smalls lands, after all the total species 80 are being sum up too) In the calculators appears ln(3)
• How does one go from a result in the ln form to a regular result