 # Linear Regression Using Detrended Data

Hi Everyone, Please bear to go through this detailed problem (it is probably more statistically related), as I need your expert opinions. I am working on a project to look at the impact of climate change on agricultural yield of crops, and I was advised to detrend the yield and climate data. But the R-Squared I got from using the detrended data for regression was poor and I don't know how to continue.

Here is the original data:

``````tomatodf <- data.frame(data_list\$Tomato)
``````
``````##    Year   Yield        Tmax     Tmin        Ppt          Wspd
## 1 1961  3.10         25.2         17.3        10.6          6.6
## 2 1962  3.10         25.2         17.6        11.6          6.5
## 3 1963  4.59         24.7         16.9        11.4          6.8
## 4 1964  4.21         24.5         17.2        29.4          9.7
## 5 1965  4.33         24.6         16.8         7.3          9.8
## 6 1966  4.04         24.7         17.0        30.4          8.4
``````

I detrended using the modeling option where I regress the variables of interest using a time sequence (the years in this case), and used the residuals for the new variables data. shown below.

Detrending code for yield:

``````mod1 <- lm(Yield ~ Year, data = tomatodf)
mod2 <- lm(Yield ~ poly(Year, 2), data = tomatodf)
summary(mod1)
``````

**Code for the 4 climate data variables detrending: **

``````mod3 <- lm(Tmax_Average ~ Year, data=tomatodf)
mod4 <- lm(Tmin_Average ~ poly(Year, 2), data = tomatodf)
mod5 <- lm(Ppt_Average ~ poly(Year, 1), data = tomatodf)
mod6 <- lm(Wspd_Average ~ Year, data = tomatodf)

summary(mod3)
``````

This is the detrended data:

``````##    Year   Yield           Temp_max    Temp_min     Precpt       Windspeed
## 1 1961  0.9915214  0.51687840  0.40459257  -7.305324 -1.9856019
## 2 1962  0.3209267  0.48432072  0.71292214  -6.337402 -2.0711412
## 3 1963  1.1551298 -0.04823697  0.01993058  -6.569480 -1.7566805
## 4 1964  0.1341306 -0.28079466  0.32561792  11.398442  1.1577802
## 5 1965 -0.3720708 -0.21335235 -0.07001586 -10.733636  1.2722409
## 6 1966 -1.2734745 -0.14591003  0.13302926  12.334286 -0.1132983
``````

As a new user, I can't put more than one image, so here is the summary results for the multiple linear regression: