Linear Regression

This is an R Markdown document showing the linear regression of inches of rain to wheat production by billion bushels.

Rain <- c(31.4,30.1,27.5,31.1,30.9,34.6,31.4,32.3,34.7,34.8,30.4)
# inches of rain per year 2010-2020

Wheat <- c(2.1,1.9,2.2,2.1,2.0,2.0,2.3,1.7,1.9,1.9,1.8)
# billions of bushels wheat per year 2010-2020

BL <- lm(Rain ~ Wheat)

summary (BL)
## 
## Call:
## lm(formula = Rain ~ Wheat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.3082 -1.4288 -0.1565  1.7935  2.8953 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   40.669      7.966   5.106  0.00064 ***
## Wheat         -4.482      3.987  -1.124  0.28998    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.217 on 9 degrees of freedom
## Multiple R-squared:  0.1231, Adjusted R-squared:  0.02572 
## F-statistic: 1.264 on 1 and 9 DF,  p-value: 0.29

Linear Regression Plot

 plot(Wheat, Rain, main="Linear Regression: Rain to Wheat Production",
     xlab= "Wheat Production bn/yr", ylab="Rain (in/yr)",
     xlim = c(1.5,2.5),ylim=c(25.0,35.0))
  
abline (BL, col="red")

Residual Data Plot

relation <- lm(Rain~Wheat)

res <- residuals(relation)
res
##          1          2          3          4          5          6          7 
##  0.1435294 -2.0529412 -3.3082353 -0.1564706 -0.8047059  2.8952941  1.0400000 
##          8          9         10         11 
## -0.7494118  2.5470588  2.6470588 -2.2011765
plot(Wheat,res, main="Residual Plot")

abline (a=0, b=0)