In a residual plot of residuals $e_i$ versus fitted values $\\hat{y}_i$, the vertical spread of the residuals increases linearly with $\\hat{y}_i$ (heteroscedasticity). If the standard deviation of the residuals is $1.5$ when $\\hat{y}_i = 10.0$, what is the expected standard deviation of the residuals when $\\hat{y}_i = 40.0$ under a linear heteroscedastic model of the form $\\sigma(e) = k \\cdot \\hat{y}$?