Regression methods were used to analyze the data from a study investigating the relationship between compressive strength (x) and intrinsic permeability (y) of various concrete mixes and cures. Summary quantities were n=20, LaTeX: \sum y_i∑ y i=572, LaTeX: \sum y_i^2∑ y i 2=23,530, LaTeX: \sum x_i∑ x i=43, LaTeX: \sum x_i^2∑ x i 2=157.42 and LaTeX: \sum\left(x_i\times y_i\right)∑ ( x i × y i )=1697.80. 1. Calculate the least squares estimate of the slope of the regression line. (2 pts) 2. Calculate the least square estimate of the intercept of the regression line. (2 pts) 3. Calculate the error sum of square, SSE. (2 pts) 4. Estimate the variance of the error term, LaTeX: \epsilonϵ. (2 pts) 5. Suppose that the observed value of permeability at x= 3.5 is y=41. Calculate the value of the corresponding residual e. (2 pts)