QUESTION 1 (46]
1.1. For each of the following models state whether its parameters can be estimated
using standard linear regression techniques. If linear regression can be used, what
are the independent and dependent variables that should be used?
= a) Yi /Jo+ ePix,+e
[lJ
= --- b) Yi
1
Po+f31x,+c,
(3J
= c) Yi /Jo+ /J1x1 1 + /32xi2 where /32 is known to be 5.
[3J
1.2 A researcher is researching whether or not birds of prey exposed to pollutants lay eggs
with thinner shells. He collects a random sample of egg shells from each of 6 different
nests and tests for pollutant level, p and measures the thinning of the shell, t. the results
are shown in the table below
3
1
1
I
I
:I
~I
I
~I
~I
a) Explain why linear regression model may be appropriate to describe the relationship
between p and t.
[2J
b) Calculate the coefficient of correlation.
[SJ
c) Find the equation of the regression line.
[8J
d) The scientist reviews similar studies and finds that pollutant levels above 16 are
likely to result in the death of a chick soon after hatching. Estimate the minimum
thinning of the shell that is likely to results in the death of a chick.
[2]
1.3 Here is some SPSSoutput from the multiple linear regression with independent variables
slope, porosity, and cover.
Source DF
Model
Error
Total
Dependent variable: Soillost
Sum of squares Mean square
3
680.68178
F-
Value
10
696.58545
Pr>F
<.0001
Variable
Intercept
Slope
Porosity
Cover
Parameter Estimates
DF
Parameter Standard error t-value
1 -1.59534
-0.08841628
1 76.45678
44.29509
1 1.57585
2.154979077
1 -23.77054
-1. 78108244
Pr> it I
0.932
0.128
0.0681
0.1181
a) Complete the ANOVA table.
b) Compute coefficient of determination.
Regression Analysis and ANOVA (Course Code)
(SJ
[2]
2nd Opportunity- January 2024 2