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)
140 135
78 107
85 114
115 122
122 122
109 113
98 114
101 109
101 101
133 139
137 150
88 112
80 109
149 137
125 125
95 104
115 119
91 118
154 148
187 103
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 =