Question Set 2: Simple Linear Regression

This question set uses the same Gentoo penguins data set as above.

In Question Set 1, we used correlation analysis to determine if there is a linear relationship between two quantitative variables. Now, we will use regression analysis to BOTH determine if there is a linear relationship AND generate a predictive (regression) equation for two quantitative variables.

Use the five-step hypothesis testing procedure below to determine if bill depth (mm) can be used to predict body mass (g) in the population of all Gentoo penguins.

NOTE: For this question set, the variables of interest are body mass and bill depth (not flipper length).

Question set 2

Step 1a: Write the hypotheses

The null hypothesis is provided for you below.

H₀: ₁= 0 (i.e. the slope of the regression line is 0)

H_a: _____

Gentoo Biscoe 46.1 13.2 211 4500 female 2007 Gentoo Biscoe 50.0 16.3 230 5700 male 2007 Gentoo Biscoe 48.7 14.1 210 4450 female 2007 Gentoo Biscoe 50.0 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 49.0 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 42.0 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 15.0 215 5650 male 2007 Gentoo Biscoe 48.2 14.3 210 4600 female 2007 Gentoo Biscoe 50.0 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 17.0 230 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 44.0 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 16.0 225 5700 male 2008 Gentoo Biscoe 45.3 13.7 210 4300 female 2008 Gentoo Biscoe 49.6 15.0 216 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 15.0 225 5000 male 2008 Gentoo Biscoe 46.5 14.4 217 4900 female 2008 Gentoo Biscoe 45.0 15.4 220 5050 male 2008 Gentoo Biscoe 43.8 13.9 208 4300 female 2008 Gentoo Biscoe 45.5 15.0 220 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 15.0 223 5550 male 2008 Gentoo Biscoe 47.7 15.0 216 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 15.0 216 4700 female 2008 Gentoo Biscoe 48.6 16.0 230 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 50.0 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 14.0 212 4875 female 2009 Gentoo Biscoe 52.1 17.0 230 5550 male 2009 Gentoo Biscoe 47.5 15.0 218 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 15.0 219 4850 female 2009 Gentoo Biscoe 55.9 17.0 228 5600 male 2009 Gentoo Biscoe 47.2 15.5 215 4975 female 2009 Gentoo Biscoe 49.1 15.0 228 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 14.0 208 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 16.0 230 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