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## Statistics

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 least-squares 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 Durbin-Watson 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 2156.66 344.6 200.128 47.6527

Statistics and Probability, Statistics

• Category:- Statistics and Probability
• Reference No.:- M922836

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