Question

Please document your reasoning to get full credit fie correct answer without clear path leading to in answer will NOT be accepted). Good luck! Name: 1. Below you are given a partial computer output relating the price of a company's stock ( in dolla the Dow Jones industrial average (X), and the stack prise of the company's major competitor (X2 dollars). ANOVA Table DF Regression Residual SS MSF 2001 Total a) (5 points) What has been the sample size for this regression analysis? b) (20 points) Using a = 0.05. perform the F test to determine the overall significance of the multiple regression model. c) (5 points) Calculate the multiple coefficient of determination. Interpret its value. Page 1

Answer 1

Solution: Here concept of multiple regression is used.

Solution- and two predic tors x, and x2 We have variable Y. dependent 27 degrees of freedom for residuals df Residuals We know, that, is sample size, where, no. g predictoos. Þ is 27 27 m- 2-1 30 sample size is 30. alternative hypothesis follows: and The null indipendent varia bls fets the data H. : The model with no model well as as than intercept - only fits the data better Our model H, : model. F test statistic, shall the hypothesia be given Use test To we which follows : will Regression MS Residval (1-4-u '1-4) where, MS puyresion SS Ragression df Regression

SS Residual and Residual df Residval Residual df Regrission I prudictors no. (given in table) SS Pegression 200 = loo Regression df Residual (ziven in table) 27 SS Residual SS %3D Regression Total 308 - 200 108 108 Rusidval 27 MS Regoenion |00 25 MS Residval The valve statistic is the test 25. is given for test statistic The p-valve by, P(F> valve of test statistic) <. P- value P(F > 25) P-valve 0.0000 P- valve

follows: We make decision rule a signi- at we ruject H. foil to reject H. at a then If P-valve < x, ficane level. Otherwise, e Aignijicance level. X = 0. 05 0. 0000 P-value = have, (0.0000 < 0:05) shall there fore X = 0.05 we Since, p-value < 0.05 significonce level. is enoryh multiple regression model eject H, at evidence to there At O.05 Gonclusim- is that Gonclude overall signific ant: determination is calculated coe fficient Multiple follows: as SS Regression SSTotal R- where R2 is know as multiple cuefficient of deter- mination 200 0.6493 308 a deturmination Multiple coefficient O.6493 Interpretation - 64.93 / the variations in R2 = 0.6493 means, dependent variable and is explained by the independent ovr multiple X2 collectively in variables model. rugrumion

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