ETX1100

Topics: Regression analysis, Linear regression, Errors and residuals in statistics Pages: 11 (1178 words) Published: October 14, 2014
Tutorial 11
A11.1
Data on manatee deaths due to powerboats was used to construct a linear regression model relating these deaths to the number of registered powerboats.

Year
1977
1978
1979
1980
1981
1982
1983

Power
boats
(thousands)
447
460
481
498
513
512
526

Manatee
Deaths
13
21
24
16
24
20
15

Year
1984
1985
1986
1987
1988
1989
1990

Power
boats
(thousands)
559
585
614
645
675
711
719

Manatee
Deaths
34
33
33
39
43
50
47

The model obtained was
ˆ
y = −41.43 + 0.1249 x
ˆ
where y is the estimated number of powerboat-related deaths

when the number of registered powerboats in Florida in thousands is x.
In 1998 there were 914,535 powerboats registered in Florida. (I have been unable to find the number of registrations for other years since 1990.)
According to the model, how many deaths attributable to
powerboats would you expect in 1998?

1

In fact, in 1998 in Florida there were 66 manatee deaths attributable to watercraft, while in 1999 there were 82. (See
http://www.savethemanatee.org/newsprrecorddeaths.htm.)
Comment on these numbers in relation to your calculation.
_________________________________________________________________________________________________________ _________________________________________________________________________________________________________ _________________________________________________________________________________________________________ _________________________________________________________________________________________________________ _________________________________________________________________________________________________________

A11.2
If a contingency table has 5 row categories and 6 column categories, (a) How many degrees of freedom are there for the χ 2 test for independence?

(b) What is the critical value for the test of independence for the categories represented in the table at the 1% level of significance?

(c) And at the 5% level of significance?
(d) If the χ 2 value calculated for the test is greater than the critical value, what is your conclusion?

A11.3
Consider the following contingency table.
OBSERVED FREQUENCIES
TABLE A
M1
L1
2

Total

Total

M2
30

8

38

56
86

38
46

94
132

Conduct a test of independence at the 5% level for the L and M categories using the Table A above.

2

Part B
B11.4
Following on from A10.3 and B10.6 in Tutorial 10 (last week) [See also Excel Notes E5.4]:

SUMMARY OUTPUT
Regression Statistics
Multiple R
0.625541
R Square
0.391301
Adjusted R
Square
0.382963
Standard
Error
5.096858
Observations
75
ANOVA
df
Regression
Residual
Total

Intercept
PRICE

1
73
74
Coefficients
121.9002
-7.82907

SS
MS
F
1219.091 1219.091 46.9279
1896.391 25.97796
3115.482
Standard
Error
t Stat
P-value
6.526291 18.67832 1.59E-29
1.142865 -6.85039 1.97E-09

Significance F

1.97E-09

Upper
Lower 95%
95%
108.8933 134.9071
-10.1068 -5.55135

Lower
Upper
99.0%
99.0%
104.639 139.1614
-10.8518 -4.80635

(a) Write down the equation for the line of best fit.

(b) What is the slope of the estimated regression line? Give an interpretation of this value.
________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ (c) What is the value of the intercept of the regression line? Give an interpretation of this value and discuss whether it is meaningful in this case. 3

_______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________...
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