What's the connection between the parameter estimate being 1, and the significance of the parameter estimate?

The information you gave simply shows that the coefficient (b=0.971) lies within the CI interval (0.871-1.072), and merely that information does not say anything about significance of the coefficient. To judge whether the coefficient estimate is statistically significant, what level of significance are you considering - 1%, 5% or 10%? Standard practice in CI estimation and hypothesis testing uses 5 percent significance level. If the p-value is < 0.05, then your estimate is statistically significant and vice versa - this should also correspond to the calculated t-statistic or z-statistic. Please note that specification of your null hypotheses would guide inferences of your results.

Salvatore S. Mangiafico Elvis Munyaradzi Ganyaupfu sorry I asked the wrong question. I needed to know that if the upper interval of the 95% CI has exceeded 1 (as it has in this case), what does this imply as opposed to a 95% CI ranging between -1 to 1 or 0 to 1.

Sorry, I really don't understand the revised question. Why do think it matters if the CI crosses 1 or doesn't ? Is this something specific to what you are trying to do?

Navanith Manimaran ,

Thanks for the clarity.

Please note that a CI is a range of values we can be fairly sure that a true value lies in. In light of that backdrop, a larger sample size or lower variability usually results in a tighter CI with a smaller margin of error (ME). Conversely, a smaller sample size or a higher variability commonly results in a wider CI with a larger ME. Therefore, the range of the interval is determined by those properties AND the

sample size (n), sample mean, computed t-calc or Z-calc, sample standard deviation, etc.

Salvatore S. Mangiafico yes it is specific to calculating a power ratio function from log adjusted VO2peak and lean body mass obtained from children. I was told that when using the ratio standard method (ml.kg-1.min-1), regression would yield a CI that crosses 1 making it invalid. However, this same situation occurred when using allometry to scale the data and that is where my original question came from.

Okay. I probably can't comment on the calculation of the power ratio function. But I will note that the width of the CI can change. As Elvis Munyaradzi Ganyaupfu noted, using a larger sample size may narrow the CI. But also, the level of the confidence interval will change the width. What if you used a 99% confidence interval, or an 80% confidence interval? Or a 60% confidence interval? If those don't cross 1, does this change your conclusion?

Salvatore S. Mangiafico yes if the CI is below 1 then the b parameter can be used to calculate the power function ratio but it needs to be set at 95% for this case. Thank you Salvatore S. Mangiafico and Elvis Munyaradzi Ganyaupfu for your help.