Casting aluminum

(a) Describe what the scatterplot tells you about the relationship between cylinder wall thickness and gate velocity.

(b) What is the equation of the least-squares regression line? Define any variables you use.

(c) One of the cylinders in the sample had a wall thickness of 0.4 inches. The gate velocity chosen for this cylinder was 104.8 feet per second.

Does the regression line in part

(b) overpredict or underpredict the gate velocity for this cylinder? By how much? Show your work.

(d) Is a linear model appropriate in this setting? Justify your answer with appropriate evidence.

(e) Interpret each of the following in context:

(i) The slope

(ii) s

(iii) r2

(iv) The standard error of the slope