Predicting Chl-a from T-Chla. The regression explains 99% of the varibility, so we can confidently replace missing values with predicted CHL

## 
## Call:
## lm(formula = CHL ~ TCHL, data = us)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -157.193   -0.466    0.028    0.515   33.651 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.0000799  0.0398553  -0.002    0.998    
## TCHL         0.9147471  0.0009575 955.385   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.261 on 10383 degrees of freedom
##   (3403 observations deleted due to missingness)
## Multiple R-squared:  0.9888, Adjusted R-squared:  0.9888 
## F-statistic: 9.128e+05 on 1 and 10383 DF,  p-value: < 2.2e-16

Filter some type in the data (i.e. month =26), missepelling of one lake name (“Whitecell” = “Whitesell”) and log transform predictors.

Do linear regression individually for each lake, plot the intercept and estimate for logTP (slope) for each lake. Then collate the intercept, slope, rsquared and p-value for each lake regression in Lake_LM_sum (see summary table).

## Loading required package: Matrix
## 
## Attaching package: 'Matrix'
## The following object is masked from 'package:tidyr':
## 
##     expand
## The following objects are masked from 'package:base':
## 
##     crossprod, tcrossprod

##      Lake             Intercept           Estimate      
##  Length:234         Min.   :-20.7673   Min.   :-3.8067  
##  Class :character   1st Qu.: -3.1511   1st Qu.: 0.5355  
##  Mode  :character   Median : -1.3141   Median : 1.1049  
##                     Mean   : -1.1796   Mean   : 1.0404  
##                     3rd Qu.:  0.4083   3rd Qu.: 1.5864  
##                     Max.   : 17.9346   Max.   : 5.2941  
##       Rsq                  p            
##  Min.   :0.0001646   Min.   :0.0000000  
##  1st Qu.:0.1607596   1st Qu.:0.0000193  
##  Median :0.3909025   Median :0.0055715  
##  Mean   :0.4066013   Mean   :0.1461939  
##  3rd Qu.:0.6320154   3rd Qu.:0.1778342  
##  Max.   :0.9878182   Max.   :0.9806943

Filter lakes with slopes <0 (i.e. negative relationships with TP) and plot the CHL:TP ratio in response to NTU+NVSS as a measure of turbidity.