Home Work Assignment 4
for MSIS 385 section 02
Last modified on 4/9/99 11:26 PM
Due April 13 1999 in class
Make sure to put your name, student ID number and the date on
the Assignment. The results of questions 1, 2 and 10 are Excel
worksheets which should be turned in on a diskette. Make sure
to put your name ID and Homework number 4 on the diskette's
label.
Note:
Question 1
Simple
nonlinear
regression
with Excel
Question 2
This question is the continuation of Question 9d. Use the data in the
same world bank Excel spreadsheet data sheet.
Use the adult male illiteracy rate as the dependent variable and per
capita GDP as the independent variable. Create a scatter diagram as
before. But this time add several trend lines (i.e. regression curves)
that fit the data best. Specifically experiment with the following chart
types: linear, polynomial of degree 6, and logarithmic. Which one
gets the best fit? What is your criterion for "best fit"? Use the
following guidelines to draw the trend lines:

On the same scatter diagram draw all four of trend lines.

Use different colors for each curve.

Make sure for each curve you print its equation and R2; use
the same color for each equation as its corresponding curve.
(Thus if the logarithmic curve is drawn in red, then the
equation and R2 of the logarithmic curve should also be in
red) To change the color of an object, be it the curve or the
box containing its equation, you may right click on the object
and choose format and within the format menu choose the
color option to set the color.

Save the charts in separate worksheet named Question 1.
Recordings of the levels of pollutants and various meteorological
conditions are made hourly at several stations by the Los Angles
Pollution Control District. This agency attempts agency attempts to
Multiple
regression
with Excel
construct mathematical/statistical models to predict pollution levels
and to gain a better understanding of the complexities of air pollution.
Obviously very large quantities of data are collected and analyzed,
but only a small set will be considered for this problem. The table in
the file "polute.xls" gives the maximum level of an oxidant (a
photochemical pollutant) and the morning averages of four
meteorological variables: wind speed, temperature, humidity, and
insolation (a measure of the amount of sunlight.) The data cover 30
days during one summer.
Examine the relationship of oxidant level to each of the four
meteorological variables. To do so you need to click on tools menu
and choose data analysis and then within that choose regression.
Then choose the column that contains the oxidant as the dependent
variable and the block of all data that contain meteorological data as
the independent variable. Within the regression tool menu enter the
appropriate cell addresses in "input X range" and "input Y range".
Also set the confidence level to 99%; Excel will report both the
default 95% and 99% significance levels. Check the labels button. In
then output range area check the "new worksheet ply" button so that
your results are produced in a new worksheet. In the residuals area
check "residuals", "residuals plot" and "line fit plots". Leave all other
buttons unchecked. Check OK to get your new worksheet with your
charts and statistical analysis. Rename the worksheet to "Question
2a".
Answer the following questions by referring to the data generated by
Excel:
a) For each of the four independent variables let the Null hypothesis
indicate that the slope equals zero, that is the there is no
relationship between that variable and level of the oxidant. (Thus
you will have four different null hypotheses for four different
tests, one for each independent variable.) For each one let the
alternative hypothesis be that the slope is different from zero
implying that there is a relationship between that variable and the
level of pollutant in the air. Based on confidence levels of 95%
and 99% decide for each variable if the null hypothesis is to be
rejected or not.
b) Look at the confidence intervals (both 95% and 99% significance
levels) and report how by just looking at these values you can
decide if the null hypothesis is rejected or not for each of the
independent variables.
c) By looking at the data generated in part a) which one of the four
meteorological factors seem most important? List these factors in
order of decreasing importance. Next repeat part a) but only
running the multiple regression on the two most important
factors. Compare the R2 and the t-significance levels and P-values
of the two most important parameters to their corresponding
values in part a). Can you explain the difference?
Question 3
Do problem 11.6 on page 390.
Question 4
Do problem 11.10 on page 392.
Question 5
Do problem 11.13 on page 392.
Question 6
Do Problem 11.21 on page 396.
Question 7
Do problem 11.30 on page 399.
Question 8
Do problem 11.37 on page 401.
Question 9
Do problems 11.45, 11.46, 11.47 and 11.48
Question 10
Use Excel to do problem 12.2 on page 429.
Question 11
Do problem 12.5 on page 430