The Regression Analysis - Research Paper Example

RENTLAND.MTW Alfalfa is one of the crops used to determine the good production of dairy cows. It is considered that the rent of the land planted toalfalfa is relative to the other agricultural purposes would be higher in the area with high density of dairy cows and lower in counties where liming is required. The basis of this can be proving by using the regression analysis, this study shows the relationship of the rent of land to the other factors, based on the data provided. The Analysis of relationship between the fertilizer and the variety of corn in farm land will be analyzed by using one way ANOVA test. This will give us some factors of which is the best fertilizer to be used and the population means yield of corn. Regression Analysis: Average1 versus Average2 The regression equation is Average1 = 3.73 + 0.879 Average2 Predictor Coef SE Coef T P Constant 3.734 3.858 0.97 0.339 Average2 0.87913 0.07824 11.24 0.000 S = 10.7102 R-Sq = 76.9% R-Sq(adj) = 76.3% Analysis of Variance Source DF SS MS F P Regression 1 14483 14483 126.26 0.000 Residual Error 38 4359 115 Total 39 18842 Regression Analysis: Average1 versus Density The regression equation is Average1 = 34.3 + 0.417 Density Predictor Coef SE Coef T P Constant 34.315 6.120 5.61 0.000 Density 0.4173 0.2537 1.65 0.108 S = 21.5142 R-Sq = 6.6% R-Sq(adj) = 4.2% Analysis of Variance Source DF SS MS F P Regression 1 1252.9 1252.9 2.71 0.108 Residual Error 38 17588.7 462.9 Total 39 18841.6 Regression Analysis: Average1 versus Pasture The regression equation is Average1 = 53.7 - 61.8 Pasture Predictor Coef SE Coef T P Constant 53.691 5.144 10.44 0.000 Pasture -61.83 22.55 -2.74 0.009 S = 20.3456 R-Sq = 16.5% R-Sq(adj) = 14.3% The value of coefficient of determination for the average rent per acre planted to alfalfa to average rent paid for all tillable land is 16.5%. Analysis of Variance Source DF SS MS F P Regression 1 3111.7 3111.7 7.52 0.009 Residual Error 38 15729.9 413.9 Total 39 18841.6 Regression Analysis: Average1 versus Liming The regression equation is Average1 = 46.2 - 7.80 Liming Predictor Coef SE Coef T P Constant 46.195 4.671 9.89 0.000 Liming -7.798 6.963 -1.12 0.270 S = 21.9087 R-Sq = 3.2% R-Sq(adj) = 0.6% The value of coefficient of determination for the average rent per acre planted to alfalfa to average rent paid for all tillable land is 3.2%. Analysis of Variance Source DF SS MS F P Regression 1 602.0 602.0 1.25 0.270 Residual Error 38 18239.6 480.0 Total 39 18841.6 For the average rent per acre planted to alfalfa and the average rent paid for all tillable land we found that the coefficient of determination is r2= 0.769, indicating that the ratio of explained variation in y to the total variation in y is 0.709. We can therefore state that 76.9% of the total variation in average rent per acre planted to alfalfa can be explained by the variation in average rent paid for all tillable land. The value of coefficient of determination for the average rent per acre planted to alfalfa and density of dairy cows is r2 = 0.066. This means that the total variation in average rent per acre planted to alfalfa and the density of dairy cow (number per square miles) is 6.6%. In comparing the average rent per acre planted to alfalfa to proportion of farm land in the country need for Pasteur the value of coefficient of determination is r2= .165. This means that for the average rent per acre planted to alfalfa there is 16.5% proportion to farmland in the country need for pasteur. The value of coefficient of determination for the average rent per acre plan planted to alfalfa to average rent paid for all tillable land is r2= .032, which means that 3.2% of the average rent per acre plan planted to alfalfa is proportion to the average rent paid for all tillable land. One-way ANOVA: VA, VB, VC, VD Source DF SS MS F P Factor 3 343 114 0.50 0.688 Error 12 2735 228 Total 15 3078 S = 15.10 R-Sq = 11.15% R-Sq(adj) = 0.00% Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev -+---------+---------+---------+-------- VA 4 39.00 8.79 (------------*-------------) VB 4 47.88 23.59 (-------------*-------------) VC 4 50.17 15.67 (-------------*-------------) VD 4 50.33 5.71 (-------------*-------------) -+---------+---------+---------+-------- 24 36 48 60 Pooled StDev = 15.10 Tukey 95% Simultaneous Confidence Intervals All Pairwise Comparisons Individual confidence level = 98.83% VA subtracted from: Lower Center Upper -------+---------+---------+---------+-- VB -22.82 8.88 40.58 (--------------*---------------) VC -20.54 11.17 42.87 (---------------*--------------) VD -20.37 11.34 43.04 (---------------*---------------) -------+---------+---------+---------+-- -20 0 20 40 VB subtracted from: Lower Center Upper -------+---------+---------+---------+-- VC -29.42 2.29 33.99 (---------------*---------------) VD -29.25 2.46 34.16 (---------------*---------------) -------+---------+---------+---------+-- -20 0 20 40 VC subtracted from: Lower Center Upper -------+---------+---------+---------+-- VD -31.54 0.17 31.87 (---------------*---------------) -------+---------+---------+---------+-- -20 0 20 40 The result from the table shows that there is no significant difference between the different set of variety of corn. Because the f computed value 0.5 is lesser than the critical F value which is equal to 3.4903. This shows that even though they differ in variety the always yield in a given plot. On the basis of their standard deviation by analyzing the growth of corn, variety D is greater than the other variety. Based on the result the mean population yield of a corn can be the same for all varieties of corn. There will be difference in the yield if we consider other sources of their differences example is the fertilizer that they are using. One-way ANOVA: F1, F2, F3, F4 Source DF SS MS F P Factor 3 643 214 1.06 0.404 Error 12 2435 203 Total 15 3078 S = 14.25 R-Sq = 20.88% R-Sq(adj) = 1.10% Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev -----+---------+---------+---------+---- F1 4 49.33 7.89 (---------*---------) F2 4 45.29 15.82 (---------*----------) F3 4 55.08 21.06 (----------*---------) F4 4 37.67 7.47 (---------*---------) -----+---------+---------+---------+---- 30 45 60 7 Pooled StDev = 14.25 Tukey 95% Simultaneous Confidence Intervals All Pairwise Comparisons Individual confidence level = 98.83% F1 subtracted from: Lower Center Upper ---------+---------+---------+---------+ F2 -33.96 -4.04 25.87 (-----------*-----------) F3 -24.17 5.75 35.67 (-----------*-----------) F4 -41.58 -11.67 18.25 (-----------*-----------) ---------+---------+---------+---------+ -25 0 25 50 F2 subtracted from: Lower Center Upper ---------+---------+---------+---------+ F3 -20.12 9.79 39.71 (-----------*-----------) F4 -37.54 -7.62 22.29 (-----------*-----------) ---------+---------+---------+---------+ -25 0 25 50 F3 subtracted from: Lower Center Upper ---------+---------+---------+---------+ F4 -47.33 -17.42 12.50 (-----------*-----------) ---------+---------+---------+---------+ -25 0 25 50 Residual Plots for F1, F2, F3, F4 The data shows that the computed value for f ratio is 1.06 which is smaller than the tabulated f value which is 3.4903. This mean that there is no difference in using different fertilizer based on the population mean yields of corn. But if we look its standard deviation the value of fertilizer no. 4 is 7.47 which is smaller than the other SD of other fertilizer used. Based on the result we conclude that the population means yield of corn is the same as to the different fertilizer used. There will be difference in yielding if we consider the process of using the fertilizer and other sources which may affect the yielding of corn. Based on the descriptive statically result, the effect of using different fertilizer in different varieties of corn is very small. They differ in their standard deviation and their mean. Due to this we can say that there is an interaction between the different fertilizers used in the variety of corn. Using one way ANOVA test to determine the differences of fertilizer used, the result is that there is no clear evidence of who is the best fertilizer. But if we used the descriptive analysis it is obviously fertilizer 4 is the consistent fertilizer and effective to use in yielding of corn. Read More