Linear regression-bud set versus daylight length
The scatter plots show that there is a linear relationship between daylight length and bud set score. Linear regression will show the relation with significance at 5 % level.
1. Bud set score does not follow a good normality based on the Shapiro-Wilk normality test ( p-value = 0.009224). Then transform bud set score in to the square of bud set score to meet the normality assumption for regression.
2. Residual plot shows some variance not very equal. But the spread of points are still relatively even above and below the RES=0 line. All assumptions are met thus unbiased linear regression can be finished.
3. Pearson’s correlation coefficient is 0.76864580 for squared bud set score versus daylight length one day before the bud set records, which is on September 13th, 2000. The coefficient shows a relatively significant relationship.
1. Bud set score does not follow a good normality based on the Shapiro-Wilk normality test ( p-value = 0.009224). Then transform bud set score in to the square of bud set score to meet the normality assumption for regression.
2. Residual plot shows some variance not very equal. But the spread of points are still relatively even above and below the RES=0 line. All assumptions are met thus unbiased linear regression can be finished.
3. Pearson’s correlation coefficient is 0.76864580 for squared bud set score versus daylight length one day before the bud set records, which is on September 13th, 2000. The coefficient shows a relatively significant relationship.
The equation below is the regression for bud set score in 2000 versus daylight length of provenance origins in the Athabasca trials. The R square adjusted is 0.5808. The relation is significant at the 0.05 level. The linear regression for bud set score versus latitude or longitude are also significant as following. But the elevation is not significantly related to bud set score.
With respect of latitude, longitude, and elevation, linear regression show that there are significant relations between bud set score and these variables (R squared more than 0.5), other than bud set time versus elevation (R squared is 0.09). The residual plot set show the normality and equal variance of the regression. The assumptions of simple linear regression are met.
Multiple linear regression--bud set versus climate variables
The scatter plot show that there may be a correlation between bud set score versus climatic variables such as average temperature in autumn (TAV_at), average temperature in August (TAV08), maximum temperature in September (TMX09) and so on. A multiple linear regression will show the relation with significance at 5 % level.
1. Bud set score does not follow a good normality based on the Shapiro-Wilk normality test ( p-value = 0.009224). Then transform bud set score in to the square of bud set score to meet the normality assumption for regression.
2. Residual plot shows some variance not very equal. The spread of points are still relatively even above and below the RES=0 line. All assumptions are not well met thus multiple linear regression can be invalidated.
3. A stepwised regression is used starting from
bud set squared ~DD.5+eFFP+TAV_at+TMN_at+TAV08+TMX09 and ending up with the function as following. More than 60% of the y variances can be explained with the function. However, as the assumptions are not well met, thus another manual step wised regression is done for bud set squared versus environmental variables.
1. Bud set score does not follow a good normality based on the Shapiro-Wilk normality test ( p-value = 0.009224). Then transform bud set score in to the square of bud set score to meet the normality assumption for regression.
2. Residual plot shows some variance not very equal. The spread of points are still relatively even above and below the RES=0 line. All assumptions are not well met thus multiple linear regression can be invalidated.
3. A stepwised regression is used starting from
bud set squared ~DD.5+eFFP+TAV_at+TMN_at+TAV08+TMX09 and ending up with the function as following. More than 60% of the y variances can be explained with the function. However, as the assumptions are not well met, thus another manual step wised regression is done for bud set squared versus environmental variables.
Residual plot of the regression
A residual plot set show the normality and equal variance assumptions of the regression are not well met.
Functions of other environmental variable combinations are listed below. This regression is manually stepwised by choosing combinations of environmental variables versus bud set score squared with higher Pearson's correlation coefficents. TAV-at and TAV08 are more likely to have significant relation combined with each other or with latitude. The regression is significant at 5% level.
