# ETX1100

**Topics:**Regression analysis, Linear regression, Errors and residuals in statistics

**Pages:**11 (1178 words)

**Published:**October 14, 2014

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

_______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________...

Continue Reading

Please join StudyMode to read the full document