September 2019

height = intercept + 0.2 back + error

Data plots

across ~~ back

height ~ across

height ~ back

Model fit

height ~ across

## 
## Call:
## lm(formula = height ~ across, data = dat)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.83664 -0.28953 -0.02315  0.34661  0.67719 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.03626    0.16433  18.477   <2e-16 ***
## across      -0.02034    0.03617  -0.562    0.579    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3859 on 26 degrees of freedom
## Multiple R-squared:  0.01201,    Adjusted R-squared:  -0.02599 
## F-statistic: 0.3162 on 1 and 26 DF,  p-value: 0.5787

height ~ back

## 
## Call:
## lm(formula = height ~ back, data = dat)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.35187 -0.10475 -0.00006  0.08290  0.36428 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   2.2412     0.0833  26.907  < 2e-16 ***
## back          0.1583     0.0168   9.419 7.26e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1848 on 26 degrees of freedom
## Multiple R-squared:  0.7734, Adjusted R-squared:  0.7646 
## F-statistic: 88.72 on 1 and 26 DF,  p-value: 7.262e-10

height ~ across + back

## 
## Call:
## lm(formula = height ~ across + back, data = dat)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.33980 -0.09659 -0.01603  0.07463  0.39512 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.29287    0.11290  20.309  < 2e-16 ***
## across      -0.01203    0.01752  -0.686    0.499    
## back         0.15768    0.01700   9.275 1.43e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1868 on 25 degrees of freedom
## Multiple R-squared:  0.7775, Adjusted R-squared:  0.7598 
## F-statistic: 43.69 on 2 and 25 DF,  p-value: 6.925e-09

Correlated predictors

height = intercept + 0.2 back + error

across ~~ back

height ~ across

## 
## Call:
## lm(formula = height ~ across, data = dat)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.31673 -0.19924  0.00421  0.18760  0.40666 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.82617    0.11672  15.646 1.58e-11 ***
## across       0.16923    0.02255   7.505 8.62e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2372 on 17 degrees of freedom
## Multiple R-squared:  0.7681, Adjusted R-squared:  0.7545 
## F-statistic: 56.32 on 1 and 17 DF,  p-value: 8.619e-07

height ~ back

## 
## Call:
## lm(formula = height ~ back, data = dat)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.26514 -0.17160 -0.00382  0.12265  0.50857 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.86453    0.09906  18.822 8.05e-13 ***
## back         0.20887    0.02441   8.558 1.44e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2138 on 17 degrees of freedom
## Multiple R-squared:  0.8116, Adjusted R-squared:  0.8005 
## F-statistic: 73.24 on 1 and 17 DF,  p-value: 1.441e-07

height ~ across + back