The student pilot reported that while on a solo cross country flight, after he landed at his destination, the weather degraded. He reported that he called his flight instructor and the flight instructor told him to wait out the weather. About three hours later, his flight instructor called him to check on the weather conditions. The student pilot reported that he checked the local weather reporting station, "but everything [was] missing" (referring to the weather information). His flight instructor told him to "get back and check the weather and I'll call you back". The student pilot interpreted that as "[it's] ok to takeoff". During the takeoff roll the airplane veered off the runway to the left and impacted a ditch. The flight school President reported no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation. A review of recorded data from a weather observation station located about 1.6 miles to the northeast, revealed that, about the time of the accident the wind was 360 degrees true at 3 knots. The airplane departed on runway 36.