Solved Problems

Find the regression equation ($\hat{y} = b_0 + b_1 x$) for the following data on traffic volume ($X$, in 1000s) and accident rate ($Y$):

Using the data from Problem 1 on traffic volume ($X$) and accident rate ($Y$), calculate the Pearson correlation coefficient ($r$) to determine the strength and direction of the linear relationship. Additional sum needed: $\sum y^2 = 2^2 + 5^2 + 8^2 + 10^2 + 14^2 = 389$.

A structural engineer uses multiple linear regression to model the deflection of a beam ($Y$, in mm) based on two independent variables: the applied load ($X_1$, in kN) and the length of the beam ($X_2$, in meters). The resulting model is:

Additionally, the $R^2$ (coefficient of determination) for the model is $0.85$. Interpret the coefficients and the $R^2$ value.