Introduction to Geostatistics – Exercises 8 Regression

Introduction to Geostatistics – Exercises
Katharina Henneböhl, Kristina Helle, Benedikt Gräler
Institut für Geoinformatik, Universität Münster
1. Juni 2011
Deadline: Monday 6. June 2011, 21:00 by email to your tutors/lecturers
Points: 12
Use the studNoEx dataset from the course website.
Linear regression by hand
In the next exercises you shall do regression by hand. To simplify computation use only the 8 students
with Semester > 4. The model we investigate is
YW eight = α + βXLength + Exercise 8.1 [2 points] Plot the data X = Length, Y = W eight by hand and draw the regression line
by eye. Write down the criterion for placing the regression line and explain what the residuals are.
Exercise 8.2 [3 points] Calculate the regression coefficients by hand (or with a calculator). Use a
table for the intermediate results as in the lecture (slide 9.8). Write down the regression equation with
the resulting coefficients.
Give also the appropriate R command to compute the coefficients. Compare the results to the ones from
the manual computation.
Use the model computed above for the next exercises.
Exercise 8.3 [1 point] What do a and b mean in terms of body length and weight?
Exercise 8.4 [2 points] What average weight do you expect for a person of 1.90 m?
Is this model appropriate to determine the weight of a child of 90 cm height? Point out possible problems
and suggest solutions. Can you solve the problems by using more data, e.g. all data from the studNoEx
Exercise 8.5 [2 points] Compute (by R) the regression model for the students above fourth semester
as above and the one for the full dataset. For both determine the 95% confidence interval for β. Are
there possible values for β that are contained in both intervals? How do the intervals differ?
Exercise 8.6 [2 points] Compute and plot the confidence bands for the mean Y0 and for single values
–for the model of the full dataset. Many of the points do not fall within the small confidence band and
some do even not fall within the wide band. Give an explanation of both phenomena.