Project #9679 - regression

word equations and graphs

A group of legislators wanted to look at factors that affect the number of traffic fatalities. They collected some data for 1994 from the National Transportation Safety Board on the number of fatalities for 50 states and the District of Columbia (DC), the number of licensed drivers, the number of registered vehicles, and the number of vehicle miles traveled.

 

State

Traffic Fatalities

Licensed Drivers (thousands)

Registered Vehicles (thousands)

Vehicle Miles Traveled (millions)

AL

1083

3043

3422

48956

AK

85

443

508

4150

AZ

903

2654

2980

38774

AR

610

1770

1560

24948

CA

4226

20359

23518

271943

CO

585

2620

3144

33705

CT

310

2205

2638

27138

DE

112

512

568

7025

DC

69

366

270

3448

FL

2687

10885

10132

121989

GA

1426

4666

5638

82822

HI

122

742

781

7935

ID

249

779

1062

11652

IL

1554

7548

8331

92316

IN

974

3834

4850

62108

IA

478

1921

2929

25737

KS

442

1794

1965

24678

KY

778

2498

2615

39822

LA

838

2606

3242

37430

ME

188

916

1071

12469

MD

651

3311

3543

44165

MA

440

4209

3956

46990

MI

1419

6602

7599

85183

MN

644

2668

3869

43317

MS

791

1659

2056

28548

MO

1089

3512

4179

57288

MT

202

536

967

9116

NE

271

1154

1490

15466

NV

294

987

983

13019

NH

119

878

1013

10501

NJ

761

5521

5752

60466

NM

447

1162

1472

20480

NY

1658

10444

10428

112970

NC

1431

4779

5462

71928

ND

88

443

687

6338

OH

1371

7722

9647

98200

OK

687

2363

2863

36980

OR

490

2401

2748

29453

PA

1441

8146

8557

92347

RI

63

682

728

7095

SC

847

2458

2764

37245

SD

154

512

845

7631

TN

1214

3583

5150

54524

TX

3186

12012

13287

178348

UT

342

1203

1381

18078

VT

77

435

502

6152

VA

930

4631

5593

67609

WA

638

3741

4654

47428

WV

356

1317

1375

17112

WI

712

3542

4044

50273

WY

144

354

583

6689

 

 

(a)    Copy and paste the data from this document to an Excel file. Select the Number of Traffic Fatalities as the dependent variable. Do a scatter plot between the Number of Traffic Fatalities and Number of licensed drivers (in thousands), a second scatter plot between the Number of Traffic Fatalities and the Number of Registered Vehicles (in thousands) and a third scatter plot between the Number of Traffic Fatalities and the Number of Vehicle Miles Traveled (in millions). Paste the scatter plots below and discuss the nature of the relationship based on the scatter plots. Note: Follow the instructions given in module 4 to do the scatter plots.

(b)   Select the Number of Traffic Fatalities as the dependent variable and the Number of licensed drivers (in thousands), the Number of Registered Vehicles (in thousands) and the Number of Vehicle Miles Traveled (in millions) as independent variables. Conduct multiple regression using Excel. Paste the output report below. Note: Follow the instructions given in module 4 to conduct simple regression. At the step where you specify the input data range, instead of selecting the data for one independent variable, select data for all the independent variables.

(c)    Write the equation from the regression output report. If you are using symbols in the equation for the variables, do define the symbols before using the symbols in the equation. Provide clear and complete interpretation of the coefficients b1, b2 and b3 in the equation. There is no need to interpret b0.

(d)   What is the value of R2 for this model? Do you think that the model does a good job of explaining the variation in the number of traffic fatalities? Why or why not?

(e)   Set up the hypotheses to test whether the model is significant. Is the regression model significant at 0.05 as the level of significance? What does this mean?

(f)     Set up the hypotheses to test for each of the regression coefficients individually and perform the test at the 0.05 level of significance.

(g)    What are your conclusions from the tests on individual coefficients? Do any variables need to be dropped? If so, rerun the regression and determine the final regression equation. Note: drop the variables one at a time starting with the variable with the largest p-value (least significant), rerun the regression without the data for the dropped variable, check the p-values again and continue the process until all p-values (other than for the intercept term) are less than the level of significance.

(h)   Compare the final equation with the first regression equation. What recommendations do you have about using the final equation? Give reasons for your answer.

(i)      Suppose there was a state with the following values of the independent variables: Number of Licensed Drivers (in thousands) = 3,500, Number of Registered Vehicles (in thousands) = 4,000 and Number of Vehicle Miles Traveled (in millions) = 45,000. Determine and interpret the predicted value of the number of traffic fatalities.

Subject Mathematics
Due By (Pacific Time) 07/24/2013 09:00 pm
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