odev

#linear regression with & with out interception #1 WITH interception

agey <- c(1, 4, 8, 10, 15, 18, 20, 25) 
sizex1 <- c(10, 20, 25, 28, 30, 40, 60, 100)
foodx2 <- c(1, 1, 2, 4, 5, 2, 4, 7) 

lm(agey ~ sizex1 + foodx2)

## 
## Call:
## lm(formula = agey ~ sizex1 + foodx2)
## 
## Coefficients:
## (Intercept)       sizex1       foodx2  
##      1.7081       0.2049       0.8929

summary(lm(agey ~ sizex1 + foodx2))

## 
## Call:
## lm(formula = agey ~ sizex1 + foodx2)
## 
## Residuals:
##       1       2       3       4       5       6       7       8 
## -3.6496 -2.6981 -0.6153 -1.0157  2.6817  6.3119  2.4290 -3.4439 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  1.70814    2.84632   0.600   0.5746  
## sizex1       0.20485    0.09341   2.193   0.0798 .
## foodx2       0.89292    1.26340   0.707   0.5113  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.167 on 5 degrees of freedom
## Multiple R-squared:  0.8191, Adjusted R-squared:  0.7468 
## F-statistic: 11.32 on 2 and 5 DF,  p-value: 0.01392

head(agey)

## [1]  1  4  8 10 15 18

tail(foodx2)

## [1] 2 4 5 2 4 7

plot(x = agey, y = foodx2 + sizex1, col="red")

#2 linear regression WITHOUT intercept

summary(lm(agey ~ sizex1 + foodx2 - 1))

## 
## Call:
## lm(formula = agey ~ sizex1 + foodx2 - 1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.5322 -1.6484 -0.1989  2.5562  7.1463 
## 
## Coefficients:
##        Estimate Std. Error t value Pr(>|t|)  
## sizex1  0.21139    0.08768   2.411   0.0525 .
## foodx2  1.19899    1.09252   1.097   0.3145  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.938 on 6 degrees of freedom
## Multiple R-squared:  0.947,  Adjusted R-squared:  0.9293 
## F-statistic: 53.58 on 2 and 6 DF,  p-value: 0.0001491

summary(lm(formula = agey ~ 0 + sizex1 + foodx2))

## 
## Call:
## lm(formula = agey ~ 0 + sizex1 + foodx2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.5322 -1.6484 -0.1989  2.5562  7.1463 
## 
## Coefficients:
##        Estimate Std. Error t value Pr(>|t|)  
## sizex1  0.21139    0.08768   2.411   0.0525 .
## foodx2  1.19899    1.09252   1.097   0.3145  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.938 on 6 degrees of freedom
## Multiple R-squared:  0.947,  Adjusted R-squared:  0.9293 
## F-statistic: 53.58 on 2 and 6 DF,  p-value: 0.0001491

lm(formula = agey ~ sizex1 + foodx2 + 0)

## 
## Call:
## lm(formula = agey ~ sizex1 + foodx2 + 0)
## 
## Coefficients:
## sizex1  foodx2  
## 0.2114  1.1990