Data on the water quality in the eastern United States was obtained by a researc

Question

Data on the water quality in the eastern United States was obtained by a researcher who wanted to ascertain whether or not the amount of particulates in water (ppm) could be accurately used to predict water quality score. Suppose we fit the following simple linear regression model:

Qualityi = ? 0 + ? 1 × particulatesi + ? i

where the deviations ?i were 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

Std. error of estimate

Constant

6.214

1.003

Particulates

?0.009

0.020

R2 = 0.005, s = 0.7896. Confidence Interval for ?1 : ?0.009 ± 0.0334

Is there strong evidence (and if so, why?) that there is a straight-line dependence between the amount of particulates and water quality?

Yes, because the confidence interval for the slope includes zero.

No, because the confidence interval for the slope includes zero.

It is impossible to say because we are not given the actual value of the correlation.

Yes, because the slope of the least-squares line is not zero.

Variable

Estimate

Std. error of estimate

Constant

6.214

1.003

Particulates

?0.009

0.020

Explanation / Answer

Confidence Interval for ?1 : ?0.009 ± 0.0334

=>(-0.0424,0.0244)

Option B) is correct.

No, because the confidence interval for the slope includes zero.

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