Simple linear regression analysis using excels.
A brokerage house wants to predict the number of trade executions per day, using the number of incoming phone calls as a predictor variable. Data were collected over a period of 35 days and are stored in the file trades.xls attached.
a. make use of the leastsquares method to compute the regression of coefficients b0 and b1.
b. Interpret the meaning of b0 and b1 in this problem.
c. find out the number of trades executed for a day in which the number of incoming calls is 2,000.
d. Should you use the model to predict the number of trades executed for a day in which the number of incoming calls is 5,000? Why or why not?
e. resolve the coefficient of determination, r2, and describe its meaning in this problem.
f. plan the residuals against the number of incoming calls and also against the days. Is there any evidence of a pattern in the residuals with either of these variables? describe.
g. resolve the DurbinWatson statistic for these data.
h. Based on the results of (6) and (7), is there reason to problem the validity of the model? describe.
i. At 0.05 level of significance, is there evidence of a linear relationship between the volume of trade executions and the number of incoming calls?
j. Construct a 95 percent confidence interval estimate of the mean number of trades executed for days in which the number of incoming calls is 2,000.
k. Construct a 95 percent prediction interval of the number of trades executed for a particular day in which the number of incoming calls is 2,000.
l. Construct a 95 percent confidence interval estimate of the population slope.
m. Based on the results of (1) through (9), do you think the brokerage house should focus on a strategy of increasing the total number of incoming calls or on a strategy that relies on trading by a small number of heavy trades? describe.
Day

Calls

Trade Executions

X

Y

X2

XY

1

2591

417

2591

417

6713281

1080447

2

2146

321

2146

321

4605316

688866

3

2185

362

2185

362

4774225

790970

4

2245

364

2245

364

5040025

817180

5

2600

442

2600

442

6760000

1149200

6

2510

386

2510

386

6300100

968860

7

2394

370

2394

370

5731236

885780

8

2486

376

2486

376

6180196

934736

9

2483

463

2483

463

6165289

1149629

10

2297

389

2297

389

5276209

893533

11

2106

302

2106

302

4435236

636012

12

2035

266

2035

266

4141225

541310

13

1936

339

1936

339

3748096

656304

14

1951

369

1951

369

3806401

719919

15

2292

403

2292

403

5253264

923676

16

2094

319

2094

319

4384836

667986

17

1897

306

1897

306

3598609

580482

18

2237

397

2237

397

5004169

888089

19

2328

365

2328

365

5419584

849720

20

2078

330

2078

330

4318084

685740

21

2134

312

2134

312

4553956

665808

22

2192

340

2192

340

4804864

745280

23

1965

339

1965

339

3861225

666135

24

2147

364

2147

364

4609609

781508

25

2015

295

2015

295

4060225

594425

26

2046

292

2046

292

4186116

597432

27

2073

379

2073

379

4297329

785667

28

2032

294

2032

294

4129024

597408

29

2108

329

2108

329

4443664

693532

30

1923

274

1923

274

3697929

526902

31

2069

326

2069

326

4280761

674494

32

2061

306

2061

306

4247721

630666

33

2010

352

2010

352

4040100

707520

34

1913

290

1913

290

3659569

554770

35

1904

283

1904

283

3625216

538832




75483

12061

164152689

26268818

Average

2156.657

344.6


200.1277

47.65266
