stat 516 hw

STAT 516 – Spring 2023 – Homework 2
Due: Thursday, January 26th
1) (5 points) One of the earliest places that regression was discussed was in a paper entitled “Typical Laws
of Heredity” that was delivered by Sir Francis Galton in 1877. Galton categorized his sweet pea plants by
the size of the seeds they produced (measuring the diameter in hundredths of a centimeter below). Using
parent pea plants of several different sizes, he arranged for 90 pea plants to be grown from each size (by
forcing several friends to help). Although several of the offspring didn’t make it, he measured the average
diameter of the peas for the plants that did survive. A portion of this data was:
Diameter of
Parent Peas
50.80
48.26
45.72
43.18
40.64
Mean Diameter of
Offspring Peas
43.36
41.58
41.66
40.97
41.07
a) Write the model equation for the linear regression predicting the mean diameter of the offspring peas from
the diameter of the parent peas. Identify the symbols you use. (What is x, the 1, etc…)
b) Use R to estimate the regression line, root mean squared error, and ANOVA table for predicting the mean
diameter of the offspring peas from the diameter of the parent peas. Give the code you used and the output.
For (c)-(e) you may assume that any assumptions were met without checking them for this problem.
c) Estimate the mean diameter of the offspring of a pea that had diameter 41.0.
d) Briefly interpret the root mean squared error in the context of the problem.
e) Say what hypotheses are being tested by the p-value in the ANOVA table and state your conclusion in
terms of the problem at the =0.05 level.
2) (5 points) Complete the following ANOVA table for a simple linear regression for predicting the weights
of ten men from their heights.
Source
Regression
Error
Total
SS
1222.38
_____
1650.00
df
_____
_____
_____
MS
______
47.513
F
______