MATH 315 Homework 08

Due 2025-11-05 by 11:59pm

1. Load the dataset on finches. Our goal is to predict winglength using tarsuslength, both measured in millimeters.

   a. Perform step 1 of any regression analysis, using ggplot2.

   b. Produce the code to fit the appropriate linear regression model to predict winglength using tarsuslength.

   c. State the null and alternative hypothesis, using appropriate statistical symbols, to see if tarsuslength is a statistically significant predictor of winglength.

   c. State in words what the alternative hypothesis means, in context of these data.

   d. Pick and write a reasonable significance value/level of significance .

   e. Report the test statistic and the p-value.

   f. Using the p-value and the level of significance, make a statistical decision about the hypothesis test.

   g. Explain what this decision means, in context of these data, using minimal statistical jargon.

   h. Interpret in context of these data the adjusted $R^2$.

   i. Interpret in context of these data the intercept.

   j. Does the intercept make sense in context of these data? Why or why not?

   k. Calculate and interpret a 98% confidence interval about slope in context of these data.

   l. Calculate and interpret a prediction for an average finch with a tarsus length of 20mm.

   m. Calculate and interpret a 90% confidence interval for a prediction for an average finch with a tarsus length of 20mm.