Chapter 12.2, Problem 15E

Values of modulus of elasticity (MOE, the ratio of stress, i.e., force per unit area, to strain, i.e., deformation per unit length, in GPa) and flexural strength (a measure of the ability to resist failure in bending, in MPa) were determined for a sample of concrete beams of a certain type, resulting in the following data (read from a graph in the article “Effects of Aggregates and Microfillers on the Flexural Properties of Concrete,” Magazine of Concrete Research, 1997: 81–98):

MOE	29.8	33.2	33.7	35.3	35.5	36.1	36.2
Strength	5.9	7.2	7.3	6.3	8.1	6.8	7.0

MOE	36.3	37.5	37.7	38.7	38.8	39.6	41.0
Strength	7.6	6.8	6.5	7.0	6.3	7.9	9.0

MOE	42.8	42.8	43.5	45.6	46.0	46.9	48.0
Strength	8.2	8.7	7.8	9.7	7.4	7.7	9.7

MOE	49.3	51.7	62.6	69.8	79.5	80.0
Strength	7.8	7.7	11.6	11.3	11.8	10.7

1. a. Construct a stem-and-leaf display of the MOE values. and comment on any interesting features.
2. b. Is the value of strength completely and uniquely determined by the value of MOE? Explain.
3. c. Use the accompanying Minitab output to obtain the equation of the least squares line for predicting (strength from modulus of elasticity, and then predict strength for a beam whose modulus of elasticity is 40. Would you feel comfortable using the least squares line to predict strength when modulus of elasticity is 100? Explain.

Predictor	Coef	stdev	t-ratio	P
Constant	3.2925	0.6008	5.48	0.000
mod elas	0.10748	0.01280	8.40	0.000

Analysis of Variance

SOURCE	DF	SS	MS	F	P
Regression	1	52.870	52.870	70.55	0.000
Error	25	18.736	0.749
Total	26	71.605

d. What are the values of SSE, SST. and the coefficient of determination? Do these values suggest that the simple linear regression model effectively describes the relationship between the two variables? Explain.