Problem 1: A torsion spring on a mousetrap is twisted through different angles.The torque vs. angle data is given below.

Assuming the torque and the angle are related via the linear relationship T=k,+k,0regress the data to the straight line model. Set up the residual function and then minimize the sum of the squares of the residuals to determine the values of ko and k, in the regressor function. In other words, derive the standard linear regression formulas and then use them on this data set. Analyze the adequacy of regression: a) Plot the data and the regressor on the same figure and comment on the visual interpretation of the fit b) Calculate the standard error of the estimate c) Calculate the coefficient of determination d) Plot residuals and mean vs. x