Question Set 2: Simple Linear Regression

This question set will use the Gentoo.csv file, which can be downloaded from the Canvas page where you downloaded this lab document. This is a subset of the Palmer Penguins dataset that we used in the last lesson. This file contains data collected from 123 Gentoo penguins from Biscoe Island. In this question set, we will be exploring the relationship between bill length and bill depth.

Artwork by @allison_horst

https://github.com/allisonhorst/palmerpenguins

A. Use the five-step hypothesis testing procedure to determine if bill_depth_mm can be used to predict bill_legnth_mm in the population of all Gentoo penguins. Don't forget to show how you checked all of the assumptions.[25 points]

Step 1: Check assumptions & write hypotheses

Step 2: Compute the test statistic

Step 3: Determine the p-value

Step 4: Decide to reject or fail to reject the null hypothesis

Step 5: State a "real world" conclusion

B. The second penguin in this sample had a bill depth of 16.3 mm. Using the regression equation you constructed in part A, compute the predicted bill length for this penguin. [10 points]

C. The second penguin in this sample had an actual bill length of 50.0 mm. Using this value and the predicted value from part B, compute the residual for the first penguin in this sample. [10 points]

D. Interpret the residual you computed in part C. [10 points]

Data Set:

species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g sex year

Gentoo Biscoe 46.1 13.2 211 4500 female 2007

Gentoo Biscoe 50 16.3 230 5700 male 2007

Gentoo Biscoe 48.7 14.1 210 4450 female 2007

Gentoo Biscoe 50 15.2 218 5700 male 2007

Gentoo Biscoe 47.6 14.5 215 5400 male 2007

Gentoo Biscoe 46.5 13.5 210 4550 female 2007

Gentoo Biscoe 45.4 14.6 211 4800 female 2007

Gentoo Biscoe 46.7 15.3 219 5200 male 2007

Gentoo Biscoe 43.3 13.4 209 4400 female 2007

Gentoo Biscoe 46.8 15.4 215 5150 male 2007

Gentoo Biscoe 40.9 13.7 214 4650 female 2007

Gentoo Biscoe 49 16.1 216 5550 male 2007

Gentoo Biscoe 45.5 13.7 214 4650 female 2007

Gentoo Biscoe 48.4 14.6 213 5850 male 2007

Gentoo Biscoe 45.8 14.6 210 4200 female 2007

Gentoo Biscoe 49.3 15.7 217 5850 male 2007

Gentoo Biscoe 42 13.5 210 4150 female 2007

Gentoo Biscoe 49.2 15.2 221 6300 male 2007

Gentoo Biscoe 46.2 14.5 209 4800 female 2007

Gentoo Biscoe 48.7 15.1 222 5350 male 2007

Gentoo Biscoe 50.2 14.3 218 5700 male 2007

Gentoo Biscoe 45.1 14.5 215 5000 female 2007

Gentoo Biscoe 46.5 14.5 213 4400 female 2007

Gentoo Biscoe 46.3 15.8 215 5050 male 2007

Gentoo Biscoe 42.9 13.1 215 5000 female 2007

Gentoo Biscoe 46.1 15.1 215 5100 male 2007

Gentoo Biscoe 44.5 14.3 216 4100 2007

Gentoo Biscoe 47.8 15 215 5650 male 2007

Gentoo Biscoe 48.2 14.3 210 4600 female 2007

Gentoo Biscoe 50 15.3 220 5550 male 2007

Gentoo Biscoe 47.3 15.3 222 5250 male 2007

Gentoo Biscoe 42.8 14.2 209 4700 female 2007

Gentoo Biscoe 45.1 14.5 207 5050 female 2007

Gentoo Biscoe 59.6 17 230 6050 male 2007

Gentoo Biscoe 49.1 14.8 220 5150 female 2008

Gentoo Biscoe 48.4 16.3 220 5400 male 2008

Gentoo Biscoe 42.6 13.7 213 4950 female 2008

Gentoo Biscoe 44.4 17.3 219 5250 male 2008

Gentoo Biscoe 44 13.6 208 4350 female 2008

Gentoo Biscoe 48.7 15.7 208 5350 male 2008

Gentoo Biscoe 42.7 13.7 208 3950 female 2008

Gentoo Biscoe 49.6 16 225 5700 male 2008

Gentoo Biscoe 45.3 13.7 210 4300 female 2008

Gentoo Biscoe 49.6 15 216 4750 male 2008

Gentoo Biscoe 50.5 15.9 222 5550 male 2008

Gentoo Biscoe 43.6 13.9 217 4900 female 2008

Gentoo Biscoe 45.5 13.9 210 4200 female 2008

Gentoo Biscoe 50.5 15.9 225 5400 male 2008

Gentoo Biscoe 44.9 13.3 213 5100 female 2008

Gentoo Biscoe 45.2 15.8 215 5300 male 2008

Gentoo Biscoe 46.6 14.2 210 4850 female 2008

Gentoo Biscoe 48.5 14.1 220 5300 male 2008

Gentoo Biscoe 45.1 14.4 210 4400 female 2008

Gentoo Biscoe 50.1 15 225 5000 male 2008

Gentoo Biscoe 46.5 14.4 217 4900 female 2008

Gentoo Biscoe 45 15.4 220 5050 male 2008

Gentoo Biscoe 43.8 13.9 208 4300 female 2008

Gentoo Biscoe 45.5 15 220 5000 male 2008

Gentoo Biscoe 43.2 14.5 208 4450 female 2008

Gentoo Biscoe 50.4 15.3 224 5550 male 2008

Gentoo Biscoe 45.3 13.8 208 4200 female 2008

Gentoo Biscoe 46.2 14.9 221 5300 male 2008

Gentoo Biscoe 45.7 13.9 214 4400 female 2008

Gentoo Biscoe 54.3 15.7 231 5650 male 2008

Gentoo Biscoe 45.8 14.2 219 4700 female 2008

Gentoo Biscoe 49.8 16.8 230 5700 male 2008

Gentoo Biscoe 46.2 14.4 214 4650 2008

Gentoo Biscoe 49.5 16.2 229 5800 male 2008

Gentoo Biscoe 43.5 14.2 220 4700 female 2008

Gentoo Biscoe 50.7 15 223 5550 male 2008

Gentoo Biscoe 47.7 15 216 4750 female 2008

Gentoo Biscoe 46.4 15.6 221 5000 male 2008

Gentoo Biscoe 48.2 15.6 221 5100 male 2008

Gentoo Biscoe 46.5 14.8 217 5200 female 2008

Gentoo Biscoe 46.4 15 216 4700 female 2008

Gentoo Biscoe 48.6 16 230 5800 male 2008

Gentoo Biscoe 47.5 14.2 209 4600 female 2008

Gentoo Biscoe 51.1 16.3 220 6000 male 2008

Gentoo Biscoe 45.2 13.8 215 4750 female 2008

Gentoo Biscoe 45.2 16.4 223 5950 male 2008

Gentoo Biscoe 49.1 14.5 212 4625 female 2009

Gentoo Biscoe 52.5 15.6 221 5450 male 2009

Gentoo Biscoe 47.4 14.6 212 4725 female 2009

Gentoo Biscoe 50 15.9 224 5350 male 2009

Gentoo Biscoe 44.9 13.8 212 4750 female 2009

Gentoo Biscoe 50.8 17.3 228 5600 male 2009

Gentoo Biscoe 43.4 14.4 218 4600 female 2009

Gentoo Biscoe 51.3 14.2 218 5300 male 2009

Gentoo Biscoe 47.5 14 212 4875 female 2009

Gentoo Biscoe 52.1 17 230 5550 male 2009

Gentoo Biscoe 47.5 15 218 4950 female 2009

Gentoo Biscoe 52.2 17.1 228 5400 male 2009

Gentoo Biscoe 45.5 14.5 212 4750 female 2009

Gentoo Biscoe 49.5 16.1 224 5650 male 2009

Gentoo Biscoe 44.5 14.7 214 4850 female 2009

Gentoo Biscoe 50.8 15.7 226 5200 male 2009

Gentoo Biscoe 49.4 15.8 216 4925 male 2009

Gentoo Biscoe 46.9 14.6 222 4875 female 2009

Gentoo Biscoe 48.4 14.4 203 4625 female 2009

Gentoo Biscoe 51.1 16.5 225 5250 male 2009

Gentoo Biscoe 48.5 15 219 4850 female 2009

Gentoo Biscoe 55.9 17 228 5600 male 2009

Gentoo Biscoe 47.2 15.5 215 4975 female 2009

Gentoo Biscoe 49.1 15 228 5500 male 2009

Gentoo Biscoe 47.3 13.8 216 4725 2009

Gentoo Biscoe 46.8 16.1 215 5500 male 2009

Gentoo Biscoe 41.7 14.7 210 4700 female 2009

Gentoo Biscoe 53.4 15.8 219 5500 male 2009

Gentoo Biscoe 43.3 14 208 4575 female 2009

Gentoo Biscoe 48.1 15.1 209 5500 male 2009

Gentoo Biscoe 50.5 15.2 216 5000 female 2009

Gentoo Biscoe 49.8 15.9 229 5950 male 2009

Gentoo Biscoe 43.5 15.2 213 4650 female 2009

Gentoo Biscoe 51.5 16.3 230 5500 male 2009

Gentoo Biscoe 46.2 14.1 217 4375 female 2009

Gentoo Biscoe 55.1 16 230 5850 male 2009

Gentoo Biscoe 44.5 15.7 217 4875 2009

Gentoo Biscoe 48.8 16.2 222 6000 male 2009

Gentoo Biscoe 47.2 13.7 214 4925 female 2009

Gentoo Biscoe 46.8 14.3 215 4850 female 2009

Gentoo Biscoe 50.4 15.7 222 5750 male 2009

Gentoo Biscoe 45.2 14.8 212 5200 female 2009

Gentoo Biscoe 49.9 16.1 213 5400 male 2009