Question

An estimated regression equation that was fit to estimate ductility in steel using its carbon content was found to be significant at alphaαequals=0.05. The​ 95% prediction interval for the ductility of steel with​ 0.5% carbon content was determined to be 0.45 to 11.59. What is the correct interpretation of this prediction​ interval?

Answer 1

Answer:

At a level of 95%, it is expected that the interval [0.45; 11.59] contains the value of the ductility in steel when its carbon content is 0.5%.

Step-by-step explanation:

Hello!

Considering the dependent variable:

Y: Ductility in steel.

And the independent variable:

X: Carbon content of the steel.

The linear regression was estimated and a prediction interval was calculated.

The prediction interval is calculated to predict a value that the variable Y (response variable) can take for a given value of the variable X (predictor variable) in the definition range of the linear regression line. Symbolically [Y/X=$x_{0}$]

In this case 95% prediction interval for Y/X=0.5

At a level of 95%, it is expected that the interval [0.45; 11.59] contains the value of the ductility in steel when its carbon content is 0.5%.

I hope it helps!