This is probably a very basic question but I cannot find the answer after experimenting a lot with it. I am using the Davis dataset from https://vincentarelbundock.github.io/Rdatasets/datasets.html (Self-Reports of Height and Weight) from 200 individuals. The question that I am trying to answer is what weight is to be expected for a specific height. My first assumption here is that weight depends on height, so I am building my model using
model=lm(davis$weight~davis$height)
As far as I understand, the independent variable is on the right whereas the dependent is on the left, right? Now, the summary of the model is
Call:
lm(formula = davis$weight ~ davis$height)
Residuals:
Min 1Q Median 3Q Max
-19.658 -5.381 -0.555 4.807 42.894
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -130.91040 11.52792 -11.36 <2e-16 ***
davis$height 1.15009 0.06749 17.04 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 8.505 on 198 degrees of freedom
Multiple R-squared: 0.5946, Adjusted R-squared: 0.5925
F-statistic: 290.4 on 1 and 198 DF, p-value: < 2.2e-16
and I am assuming that I can calculate weight = (height*1.15009) -130.91040 So, assuming this is correct, I was approached by a colleague who said that height does not predict weight but vice versa. However, changing the model to
model=lm(davis$weight~davis$height)
gives me different results when I use the values of
> summary(model)
Call:
lm(formula = davis$height ~ davis$weight)
Residuals:
Min 1Q Median 3Q Max
-18.3492 -3.7151 -0.2466 3.5349 20.8802
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 136.83054 2.02039 67.72 <2e-16 ***
davis$weight 0.51696 0.03034 17.04 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 5.702 on 198 degrees of freedom
Multiple R-squared: 0.5946, Adjusted R-squared: 0.5925
F-statistic: 290.4 on 1 and 198 DF, p-value: < 2.2e-16
and calculate height = (weight*0.517) + 136.831. For example, according to the first model, a person with 190 centimeters is expected to weigh 87.6067 kilograms where when I enter these kilos into the second model, that person is expected to be about 182 centimeters tall. Any advice or a good book where I can really understand this? Thank you in advance!
