12. Use sm=read.table(”StrengthMoE.txt”, header=T) to read the data on cement’s modulus of elasticity and strength into the R data frame sm. Copy the data into the R objects x and y by x=sm$MoE and y=sm$Strength, and use R commands to complete the following.

(a) Construct a scatterplot of the data with the fitted regression line drawn through it. Do the assumptions of the simple linear regression model, which are linearity of the regression function and homoscedasticity, appear to hold for this data set?

(b) Give the LSE for the regression coefficients, and estimate the expected strength at modulus of elasticity X = 60.

(c) Give the error sum of squares and the estimator of the intrinsic error variance.