Researchers use standards to calibrate analytical machinery in a calibration mod

Question

Researchers use standards to calibrate analytical machinery in a calibration model, where the standard is(x) and the analytical readings are (y).

I applied a linear regression model and calculated the confidence intervals of the slope and intercept.

-0.1451064       0.9929078

confint(CaContent.reg, level=.95)

(Intercept) -0.4932423 0.2030295

X__1         0.9797252 1.0060904

In context two properties could be expected, 1)If the empirical technique is any good when x=0 then y=0, if there is no substance present in the standard, the technique should not find any. 2) and the slope of the simple linear regression to equal 1. Is there evidence for either of these claims?

Explanation / Answer

1) The claim is that if x = 0, then, y = 0. So the value of intercept in this case = 0.

Since the confidence interval of intercept is (-0.49, 0.20) contains the value 0, the claim is valid. (Ans).

2) The claim is that the slope of the linear regression is = 1.

The confidence interval of slope is (0.9797, 1.0061).

Since, the confidence interval contains the value 1, the claim is valid. (Ans).

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