Question: Laboratory tests were carried out to investigate the effect of a particular additive on the strength of a concrete mix. The results are in Data sheet, where Cl contains the concentration of additive by volume) and C2 contains the corresponding strength (in Nmm-2).

(a) Plot the strength against the concentration of additive.

(b) Calculate the correlation coefficient r, and interpret this value.

(c) Fit a regression model of the form \(y=\alpha +\beta x+\gamma {{x}^{2}}+\varepsilon \), where y represents strength and x the concentration of additive. Is the coefficient of \({{x}^{2}}\) significant at the 5% level?

(d) Use your results in part (c) to select either a linear or quadratic prediction equation. Plot ^your fitted line or curve superimposed on the data points.

(e) Determine the R² coefficient for your fitted line or curve and interpret this value.

(0 Calculate a 95% confidence interval for \(\mu \) (0.75), the mean strength at a concentration of 0.75%.

(g) Use residual plots to check any assumptions that you have made in ^your tests and confidence intervals.