Introduction to regression

test
yourself
ourself
CHAPTER
3
144 Further Mathematics
4 A mining company wishes to predict its gold production output. It collected the following
data over a 9-month period.
Month (1 = January) Jan. Feb. Mar. Apr. May June July Aug. Sept.
Production (tonnes) 3 8 10.8 12 11.6 14 15.5 15 18.1
a Plot the data and fit a line, by eye, using the ‘equal number of points’ method
b State the equation of this line.
c Compute the predicted values, then residuals. Square the residuals and add them up.
d Fit a straight line to the original data using the 3-median method, stating the equation of
this line.
e Again, compute predicted values, and the residuals and square them.
f Now, use least-squares regression to find another equation for this line.
g Using the line from part f, predict the production after 12 months.
h Comment on the accuracy, usefulness and simplicity of the methods.
5 Let us pursue further the data from question 4.
a Looking at the original data set, discuss whether linearity is a reasonable assertion.
b Research into gold mines has indicated that after about 10 months, production tends not
to increase as rapidly as in earlier months. Given this information, a logarithmic
transformation is suggested. Transform the original data using this method.
c Fit a straight line to this transformed data using least-squares regression.
d Discuss whether or not this transformation has removed any non-linearity.
e Compare the prediction from question 4g with the one obtained using the logarithmic
transformation.