The current research aims to study the nature of the problem of heteroscedasticity
{instability of the error term variation in the regression analysis}, its causes and effects and to apply the most important methods for detecting this problem in the cross-sectional data. Field data were collected during the 2022/2023 agricultural season from lupine farmers in Al-Husseiniyah District, Sharkia Governorate through a questionnaire prepared for this purpose. Two samples were randomly selected, the first one included 25 farmers and the second included 102 farmers. The analysis was done using the Eviews computer program.
Tests were conducted to detect the presence of a problem of instability of the error term variation in the regression analysis for production and production factors (amount of seeds, quantity of phosphate fertilizer, number of workers, quantity of irrigation water) for the lupine crop. It was found that there is a problem of instability of the error term variation for quantity of fertilizer and amounted of seeds in the 25 farmers sample. In the case of the 102 farmers sample, there was a problem of instability for amount of phosphate fertilizer and quantity of irrigation water. It was sufficient to explain only one element (amount of fertilizer) as an example to illustrate how to detect the problem using the collected data.
In case of the 25 farmers sample, by using Park's test, the calculated T value was about 2.084 which is greater than the tabulated value that is of about 2.069, so the alternative hypothesis of the existence of the problem of instability of the error term variation is accepted. Data were processed by performing a transformation of the original model using the weighted least squares method. The calculated value of T was about 0.329, which is less than the tabulated value, so the null hypothesis is accepted where the variance of the error term is constant.
In case of the 102 farmers sample, by using the Park test, the calculated T value was about 2.005 which is greater than the tabulated T value which was about 1.984. The alternative hypothesis of the existence of the instability of error variance is accepted. After treatment, the calculated T value reached about 1.961, which is less than that of  tabular T value. Therefore, the null hypothesis that the variance of the error term is stable is accepted. From the previous results, it is cleared that there is no relationship between sample size and presence or absence of the problem of variance instability of the error term in regression analysis using cross-sectional data.
Recommendations:
The study recommends that researchers should pay attention to conducting the necessary tests to detect the problem of {heteroscedasticity} and the need to detect it and put the remedy to obtain accurate results.