MATH 456 Homework 03

Due 2026-02-10 by 11:59pm

1. Download the following dataset into your Homework 03 repository: donkeys. Here's the metadata. Please push this dataset along with your qmd file for Homework 03.

2. Use ggplot2 to make a scatter plot with Length on the x-axis and Weight on the y-axis. Draw the linear regression line on your plot.

3. Based on the plot alone, what do you expect a hypothesis test of the slope to conclude?

4. Write the null and alterative hypotheses for the hypothesis test of the slope. Pick a level of significance.

5. Produce the standard linear regression output for your hypotheses above.

6. Write down the fitted regression equation for the model above.

7. Compare the p-value to the level of significance and make a conclusion.

8. Interpret your conclusion in context of the data.

9. Interpret in context of the data.

10. Produce and interpret in context of the data a confidence interval for the slope.

11. Produce and interpret in context of the data a confidence interval for a prediction of the mean donkey Weight given a Length of .

12. Produce and interpret in context of the data a confidence interval for a prediction of a randomly selected donkey's Weight given a Length of .

13. Why is the interval in question 12. wider than that for 11.?