The following data has been collected on the relationship between concrete compressive strength, Y (MPa), and initial water to cement ratio, X (by weight); x 0.40 0.45 0.50 0.55 0.60 0.65 y 35.7 32.4 33.1 27.4 21.6 23.8 for which the following sums have been computed; X xi = 3.15, X x2 i = 1.6975, X yi = 174, X y2 i = 5203.62, X xiyi = 88.91001 a) Find the straight line of best fit through the data. b) Establish a 95% confidence interval on the true value of  0. Assume that the residuals are normally distributed with constant mean zero and constant variance. c) Is the linear relationship between Y and X significant? Test at a 95% confidence level

The following data has been collected on the relationship between concrete compressive
strength, Y (MPa), and initial water to cement ratio, X (by weight);
x 0.40 0.45 0.50 0.55 0.60 0.65
y 35.7 32.4 33.1 27.4 21.6 23.8
for which the following sums have been computed; X
xi = 3.15,
X
x2
i = 1.6975,
X
yi = 174,
X
y2
i = 5203.62,
X
xiyi = 88.91001
a) Find the straight line of best fit through the data.
b) Establish a 95% confidence interval on the true value of  0. Assume that the residuals
are normally distributed with constant mean zero and constant variance.
c) Is the linear relationship between Y and X significant? Test at a 95% confidence level.