This assignment uses the file PenguinsHW8.csv. This is a popular data set; the data were collected and

made available byDr. Kristen Gormanand thePalmer Station, Antarctica LTER, a member of the Long      Term Ecological Research Network. (Gorman, Williams, and Fraser 2014). This version of the data set was downloaded fromhere(on GitHub Gist).

The goal is to predict penguin bill length from penguin bill depth. Bill length and bill depth are shown in the image below (Image copied fromhere.)

Regression Model

1.   In the HW8 template, we provide code that creates a scatterplot of bill length on bill depth. Describe the joint relationship between bill length and bill depth.

2.   In the HW8 template, we provide code that creates a second scatterplot that adds color coded plotting symbols by species. Describe the joint relationship(s) now taking species into account.

3.   Run a linear regression of bill length on bill depth. Show the regression summary (no interpretations needed). [Hint:  refer to HW3 if you do not remember how to set up the code]

4.   Write out the regression equation using information from the regression summary. Round the regression coefficients to two decimal places.

5.   Interpret the estimated slope of the regression equation in the context of the problem.

6.   Report and interpret r2 .

7.   In the HW8 template, we provide ggplot code to create model diagnostic plots (residual plot, histogram of residuals, normal QQ plot of residuals). Do you think that the assumptions for inference are met?

Explain addressing specific assumptions.

Inference for Regression (assume all assumptions for inference are met)

8.   Find a 95% confidence interval for the slope parameter using “by-hand” calculations in a code chunk. Report and interpret the interval. [Hint: pull the numbers you need from the regression summary]

9.   Perform a hypothesis test to determine if the slope parameter is different than zero. State the hypotheses   using symbols, report the test statistic and degrees of freedom, and the p-value. Include your decision and an interpretation in the context of the problem. Use a 5% significance level. [Hint:  no code needed]

10. Observation 194 is a Gentoo penguin with a bill length of 49.6 mm and a bill depth of 16.0 mm. Using the model with rounded coefficients from problem 4, what is the residual for this penguin? Does the

model over or underestimate the bill length for this penguin?

11. Find the 99% confidence interval for the mean bill length when the bill depth is 16.0 mm. Interpret this interval.

12. Find the 99% prediction interval for a penguin that has a bill depth of 16.0 mm. Interpret this interval.