Question

A biologist is studying the levels of heavy metal contaminants among a population of the South Nakaratuan Chubby Bat. The biologist is interested in constructing a simple linear regression model to investigate the relationship between weight of an animal and the level of heavy metal contamination. In the proposed regression model the level of contaminant is the response variable and weight is the explanatory variable. The contaminant level is measured in parts per billion (ppb) and weight in grams.

A random sample of 20 individuals is selected and measurements are taken.

Contaminant study in South Nakaratuan Chubby Bat
Contaminant level (ppb)	Weight (g)
115	103
190	145
167	142
96	101
138	123
151	122
164	142
168	149
165	135
154	145
147	130
125	120
139	128
148	130
125	127
124	122
117	109
160	146
104	110
215	107

Plotting the data, the researcher notices an obvious outlier. They decide to do the regression analysis with and without the outlier and compare the results.

Calculate the slope (b₁) and intercept (b₀) of the simple regression equation using the data provided. Give your answers to 2 decimal places.

a)Slope = b₁ = ____________

b)Intercept = b₀ = ___________

Find the proportion of variation in the values of contaminant level that is explained by the regression model. Give your answer as a decimal to 2 decimal places.

c)R² = ____________

Repeat this process omitting the outlier:

d)Slope = b₁ = ____________

e)Intercept = b₀ = _________

Find the proportion of variation in the values of contaminant level that is explained by the regression model. Give your answer as a decimal to 2 decimal places.

f)R² = _________

Answer 1

applying regression on above data:

a)

Slope = b₁ = 1.04

b)

Intercept = b₀ = 13.56

c)

R² = 0.30

omitting the outlier (107,215):

d)

Slope = b₁ = 1.51

e)

Intercept = b₀ = -51.26

5)

R² = 0.82