Fitting the simple linear regression model to the n=27 observations on x = modulus of elasticity and y = flexural strength. ŷ= 7.592, sŷ=-0.179 when x = 40 and ŷ= 9.741, sŷ=0.253 for x = 60. Required:
a. Explain why sŷ is larger when x = 60 than when x = 40.
b. Calculate a confidence interval with a confidence level of 95% for the true average strength of all beams whose modulus of elasticity is 40.
c. Calculate a prediction interval with a prediction level of 95% for the strength of a single beam whose modulus of elasticity is 40.
d. If a 95% CI is calculated for true average strength when modulus of elasticity is 60, what will be the simultaneous confidence level for both this interval and the interval calculated in part (b)?