We have investigated the relationship between fathers' heights and sons' heights. But what about other parent-child relationships? Does one parent's height have a stronger association with a child height? How does the child's gender affect this relationship in heights? Are any differences that we observe statistically significant? The Galton dataset is a sample of one male and one female child from each family in the GaltonFamilies dataset. The pair column denotes whether the pair is father and daughter, father and son, mother and daughter, or mother and son. Create the galton dataset using the code below:
library(tidyverse)
library(HistData)
data("GaltonFamilies") set. seed(1)
# if you are using R 3.5 or earlier
set. seed(1, sample. kind = "Rounding")
# if you are using R 3.6 or later
galton <- GaltonFamilies %>%
group_by(family, gender) %>%
sample_n(1) %>% ungroup() %>%
gather(parent, parentHeight, father:mother) %>%
mutate(child = ifelse(gender == "female", "daughter", "son")) %>%
unite(pair, c("parent", "child"))
galton
Group by pair and summarize the number of observations in each group.
How many father-daughter pairs are in the dataset? unanswered
How many mother-son pairs are in the dataset? unanswered
Calculate the correlation coefficients for fathers and daughters, fathers and sons, mothers and daughters and mothers and sons.
Which pair has the strongest correlation in heights?
fathers and daughters
fathers and sons
mothers and daughters
mothers and sons
unanswered
Which pair has the weakest correlation in heights?
fathers and daughters
fathers and sons
mothers and daughters
mothers and sons
unanswered
The information here applies to both parts.
Use lm() and the broom package to fit regression lines for each parent-child pair type. Compute the least squares estimates, standard errors, confidence intervals and p-values for the parentHeight coefficient for each pair.
What is the estimate of the father-daughter coefficient? unanswered
For every 1-inch increase in mother's height, how many inches does the typical son's height increase?
Give your answer as a number with no units.
Which sets of parent-child heights are significantly correlated at a p-value cut off of .05?
Select ALL that apply.
father-daughter
father-son
mother-daughter
mother-son
Which of the following statements are true?
Select ALL that apply.
All of the confidence intervals overlap each other.
At least one confidence interval covers zero.
The confidence intervals involving mothers' heights are larger than the confidence intervals involving fathers' heights.
The confidence intervals involving daughters' heights are larger than the confidence intervals involving sons' heights.
The data are consistent with inheritance of height being independent of the child's gender.
The data are consistent with inheritance of height being independent of the parent's gender.