*3.4. Level 4 Results*

A multiple linear regression (MLR) analysis was performed with growing season total precipitation and maximum 4-day total precipitation as independent variables and rainfed sorghum yield as dependent variable the results of which are presented in Table 5. Although the R<sup>2</sup> values (Column 5 of Table 5) appear smaller, the regression relationships are significant, as evidenced by the F values of regression relationships presented in Table 6. Looking at the regression relationships by county, negative coefficients appear for growing season total precipitation for counties Bosque, Dallam, Hansford, and Milam only. Twenty-three out of 27 counties analyzed mathematically did not show declines in crop yield for excess precipitation when analyzed by growing season total precipitation. However, when analyzed by the maximum 4-day total precipitation, 21 out of 27 counties show negative coefficients substantiating the declines in crop yield for excess precipitation. The counties that do not show negative coefficients (with maximum 4-day total precipitation) are Bee, Bosque, Dallam, Deaf Smith, Floyd, and Hansford. Majority of the counties analyzed mathematically exhibit declining crop yields for excess precipitation showing negative coefficients mostly in maximum 4-day total precipitation and some in growing season total precipitation. Milam is the only county showing a negative coefficient for both the independent variables. Although Deaf Smith and Floyd showed some graphical relationships, they were the only counties that did not mathematically exhibit the regression relationship between the independent variables and the dependent variable.


**Table 5.** Results of multiple linear regression analysis (without principal component analysis) using annual growing season precipitation, 4-day maximum precipitation, and crop yield.

An MLR analysis like the one described above was performed with a PCA. The PCA was carried out to remove the relationship between the two independent variables. The results of the MLR are presented in Table 6; although the R2 values (Column 5 of Table 7) appear smaller, the regression relationships are significant as evidenced by the F values of regression relationships presented in Table 6. Looking at the regression relationships (with PCA) by county, negative coefficients appear for growing season total precipitation for Fannin, Hansford, Hunt, Jackson, and Milam counties only. Twenty-two out of 27 counties analyzed did not show declines in crop yield for excess precipitation when analyzed mathematically using regression relationships with growing season total precipitation and crop yields. However, when analyzed by the maximum 4-day total precipitation, 21 out of 27 counties show negative coefficients substantiating the declines in crop yield for excess precipitation. The counties that do not show negative coefficients are Bee, Bosque, Dallam, Deaf Smith, Floyd, and Hansford. Like the MLR without a PCA, most of the counties analyzed mathematically exhibit declining crop yields for excess precipitation showing negative coefficients mostly in maximum 4-day total precipitation and some in growing season total precipitation. Milam is the only county showing a negative coefficient for both the independent variables. Although showing some graphical relationships, Deaf Smith and Floyd are the only counties that did not mathematically exhibit the regression relationship between the independent variables and the dependent variable.


**Table 6.** Relevance of regression relationships.

**Table 7.** Results of multiple linear regression analysis (with PCA for removing the relationship between the two independent variables) using annual growing season precipitation, 4-day maximum precipitation, and crop yield.



**Table 7.** *Cont.*

A comparison of the R<sup>2</sup> values of regression relationships with and without PCA are presented in Table 8 which pointed out that the PCA did not offer a significant improvement in identifying relationships between excess precipitation and rainfed sorghum yield. However, there is some difference in the regression analysis results. In the regression without a PCA, only one county (Milam) did not mathematically show any declining crop yields with excess precipitation. In the regression with PCA, six out of 27 counties analyzed (Bee, Bosque, Dallam, Deaf Smith, Floyd, and Hansford) did not show declining crop yields with excess precipitation. However, the results analyzed in all four different levels point out the existence of crop yield declines with excess precipitation.


**Table 8.** R2 with and without PCA.
