### 2. r=0.1,n=500 r=0.8,n=5 a biologist is studying the levels of heavy

2. r=0.1,n=500 r=0.8,n=5 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. The SPSS output is given below. Use the output to answer the

following questions.

Model Summary

Model R R Square Adjusted R Std. Error of the Estimate Square

.921a 1 .848 .839 13.82229 a. Predictors: (Constant), weight

ANOVAa

Model Sum of Squares

Regression 1 Residual df Mean Square 18143 1 18143 3247.94781 17 Sig. 18 Total 94.96 .000b 191.05575 21391 F a. Dependent Variable: contaminant

b. Predictors: (Constant), weight

Coefficientsa

Model Unstandardized Coefficients Standardized t Sig. Coefficients

B

1 (Constant)

weight Std. Error -71.63611 28.17794 2.18277 0.22399 Beta

-2.54

.921 .021 9.74 .000 a. Dependent Variable: contaminant (a) What percent of variation in the values of contaminant level that is explained by the

linear regression model between contaminant level and weight?

(b) What is the correlation between contaminant level and weight?

(c) What is the predicted contaminant level for an animal weighted 150 grams? (d) One of the animals in this analysis had a weight of 145 grams and contaminant level of

222 ppb. What is the residual for this observation?

(e) What is least squares regression line?

(f) What is the average change in contaminant level when the weight of an animal is

increased by 1 gram?

(g) Construct a 99% confidence interval for the regression slope.

(h) The biologist wants to determine whether there is a positive linear association between

contaminant level and weight of an animal. Write down the appropriate hypotheses,

value of test statistic, degrees of freedom of the test statistic, p-value, and the

conclusion.