To examine the durability of a specific metal it is hit by c

To examine the durability of a specific metal, it is hit by certain force (in lbs) and the length of crack (in mm) is measured. A linear regression model fitted to the data gives the following output from the JMP software. Linear Fit Crack length = -12.03183 + 9.1413348eForce Summary of Fit RSquare RSquare Adj Root Mean Square Error Mean of Response Observations (or Sum Wgts) 0.841315 0.829108 18.42492 61.09885 15 Give the estimate of the following parameters (in two decimal points) Intercept = Slope = Interpret the value of the intercept in the context of the problem. How much variability in the length of crack is explained by the fitted linear model?

Solution

a)

As

Crack length = -12.03183 + 9.1413348*Force,

Then

i) Intercept = -12.03183
ii) Slope = 9.1413348

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b)

The intercept means the crack length if there was 0 force hitting the metal.

[It makes no sense though, as there is no negative length]

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c)

As

r^2 = 0.841315

Then 84.1315% of the variability in the length of crack is explained by this model. [ANSWER]