QUESTION 38

1. Data on the water quality in the eastern United States were obtained by a researcher who wanted to ascertain whether the amount of particulates in water (ppm) could be used to accurately predict the water quality score. Suppose we use the following simple linear regression model:

Quality_i=+ particulates_i+_i

where the deviations_iare assumed to be independent and Normally distributed with mean 0 and standard deviation. This model was fit to the data using the method of least squares. The following results were obtained from statistical software based on a sample of size 61:

Variable

Estimate

Standard Error of Estimate

Constant

6.214

1.003

Particulates

-0.009

0.020

r²= 0.005,s= 0.7896.

Suppose the researcher tests the following hypotheses:

H₀:₁= 0,H_a:₁0

What is the value of thetstatistic for this test?

-6.20

-0.045

0.45

6.20