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?

	A.	Yes, because the confidence interval for the slope includes zero.
	B.	No, because the confidence interval for the slope includes zero.
	C.	Yes, because the slope of the least-squares line is not zero.
	D.	It is impossible to say because we are not given the actual value of the correlation.

Answer 1

Here the answer will be NO. But I can't understand what you write about the confidence interval. But I can give you another easy logic. See here you have fitted simple regression line and the coefficient of determination is 0.005. So, the fitting is very bad. So, linearity assumption is violated. So, you can say, there is no evidence to say that there is a straight-line dependence between the amount of particulates and the water quality,

[note: If you want to know through confidence interval please retype that in the comment section I'll try to clear your understadings]