Let {Xn, n ≥ 1} be a sequence of random variables satisfying a generalized Rosenthal type inequality and stochastically dominated by a random variable X. Let {ani, 1 ≤ i ≤ n, n ≥ 1} be an array of constants. We study the Marcinkiewicz-Zygmund type strong laws for weighted sums Pn i=1 aniXi under the condition that the exponential moment of the random variable X exists. These results are the interesting supplements for some known results. As statistical applications, we provide the strong consistency of LS estimators in simple linear EV regression models with widely orthant dependent random errors.