# Quantitative analysis questions

Q1:

 A realtor in Arlington, Massachusetts, is analyzing the relationship between the sale price of a home (Price), its square footage (Sqft), the number of bedrooms (Beds), and the number of bathrooms (Baths). She collects data on 36 recent sales in Arlington in the first quarter of 2009 for the analysis. The data is shown in the accompanying table.
 Price. Sqft Beds Baths 728,000 2,399. 4. 2.5. 822,000 2,500 4 2.5 713,000 2,400 3 3.0 689,000 2,200 3 2.5 685,000 2,716 3 3.5 838,500 3,281 4 2.5 432,692 1,891 3 1.5 620,000 2,436 4 3.5 718,056 2,567 3 2.5 585,000 1,947 3 1.5 795,000 3,033 4 3.5 569,000 3,262 4 2.0 546,000 1,792 3 2.0 540,000 1,488 3 1.5 537,000 2,907 3 2.5 344,000 1,301 3 1.0 738,111 2,531 4 2.5 714,000 2,418 4 3.0 693,000 2,369 4 3.0 463,000 1,714 3 2.0 457,000 1,650 3 2.0 631,400 2,359 4 3.0 435,000 1,500 3 1.5 431,700 1,896 2 1.5 414,000 1,182 2 1.5 401,500 1,152 3 1.0 319,200 1,106 3 1.0 253,333 896 3 1.0 475,000 1,590 3 2.0 375,900 2,275 5 1.0 620,000 1,675 3 2.0 459,375 1,590 3 2.0 534,750 2,147 3 3.0 247,500 1,022 2 1.0 247,500 1,099 2 1.0 307,500 850 1 1.0
 SOURCE: http://Newenglandmoves.com.
 a. Estimate the model Price = β0 + β1Sqft + β2Beds + β3Baths + ε. (Round Coefficients and Standard Error answers to 2 decimal places. Round t Stat and p-value answers to 4 decimal places.)
 Coefficients Intercept Sqft Beds Baths
b-1. Interpret the coefficient of Sqft.
 For every additional square foot, the predicted price of a home increases by $102.74. For every additional square foot, the predicted price of a home increases by$102.74, holding number of bedrooms and bathrooms constant. For every additional square foot, the predicted price of a home increases by $102.74, holding square foot, number of bedrooms and bathrooms constant. b-2. Interpret the coefficient of Beds.  For every additional bedroom, the predicted price of a home increases by$17,808.68. For every additional bedroom, the predicted price of a home increases by $17,808.68, holding number of square feet and bathrooms constant. For every additional bedroom, the predicted price of a home increases by$17,808.68, holding square foot, number of bedrooms and bathrooms constant.
b-3. Interpret the coefficient of Baths.
 For every additional bathroom, the predicted price of a home increases by $100,202.60. For every additional bathroom, the predicted price of a home increases by$100,202.60, holding number of square feet and bedrooms constant. For every additional bathroom, the predicted price of a home increases by $100,202.60, holding square foot, number of bedrooms and bathrooms constant.  c. Predict the price of a 2,188-square-foot home with four bedrooms and three bathrooms. (Round intermediate coefficient values to 2 decimal places. Round your answer to 2 decimal places.)  Priceˆ$\stackrel{^}{\text{Price}}$$

Q2:

 (Round intermediate calculations to at least 4 decimal places.) One of the theories regarding initial public offering (IPO) pricing is that the initial return y (change from offer to open price) on an IPO depends on the price revision x (change from pre-offer to offer price). Another factor that may influence the initial return is whether or not it is a high-tech firm. The following table shows a portion of the data on 264 IPO firms from January 2001 through September 2004; the entire data set, can be found on the excel link.
 Initial Return (%) Price Revision (%) High-tech Initial Return (%) Price Revision (%) High-tech 43.95 –0.85 No 0.00 –2.18 No 13.96 –31.50 No 50.36 –50.77 Yes –8.10 –10.35 No 12.39 14.87 Yes 19.19 –53.10 Yes 0.00 –14.60 No 0.00 –8.82 No –2.39 3.10 No 6.78 0.00 Yes 23.56 2.44 No 22.74 0.00 Yes –3.27 23.02 No 0.00 –33.62 No 0.87 –11.98 Yes 0.00 –10.61 No –5.97 7.36 No 0.00 1.65 No –1.92 –31.34 No –20.99 –4.85 No 3.94 –10.11 No 3.51 11.39 No –7.46 –11.25 Yes –12.12 5.55 No –9.67 –51.97 Yes 13.11 17.00 Yes 8.83 0.00 No –11.65 –33.73 Yes 21.25 –4.89 No 28.37 –31.78 Yes 0.00 –40.16 No –9.98 3.85 Yes –3.61 –39.62 Yes 14.61 –50.83 Yes 3.97 –34.85 Yes –5.61 –11.73 No 1.49 0.00 Yes 14.96 10.04 Yes 16.05 –40.31 Yes –26.67 –7.37 No 32.85 –5.51 No –13.40 4.18 No –14.14 3.40 Yes 20.34 56.77 Yes 6.16 –28.89 Yes 19.13 –3.78 No –10.10 –7.33 No –5.86 –2.74 Yes 10.06 0.00 No 6.82 –39.87 Yes 10.04 –1.35 No 6.94 –21.44 Yes –0.99 –12.50 No 0.00 –34.29 No 6.79 11.01 Yes 7.28 11.65 No 22.88 7.09 No 13.93 0.00 Yes 19.31 –7.79 Yes 2.98 0.00 No 0.00 –13.75 Yes 10.74 –15.42 Yes 13.26 –19.45 Yes 14.70 –17.01 No 16.69 40.29 No 8.52 –3.31 No 0.00 17.75 No 4.25 –32.62 Yes 7.63 2.50 No –1.15 0.00 No –3.61 4.92 No 15.97 0.00 Yes 0.00 0.00 No –1.66 5.26 No 6.60 1.78 Yes 46.42 21.97 No 32.43 –37.24 Yes 56.46 0.81 No –6.20 –26.05 Yes 0.26 14.79 Yes 34.38 12.50 Yes 0.00 –11.83 No 6.12 –27.63 Yes 8.27 –11.79 Yes 12.66 –50.77 No 18.18 –24.13 No –2.32 –33.07 No 8.09 –0.25 No 5.62 –2.64 Yes 0.00 0.00 No 2.26 –13.24 Yes 8.05 –3.12 Yes 11.47 –21.19 No 25.23 3.66 No 9.34 –32.27 No 20.79 28.08 Yes –0.43 –5.63 No 0.00 –27.45 Yes 0.00 20.67 No 0.47 –36.72 No –1.16 13.40 No –11.89 –16.57 Yes 20.57 3.10 No 22.68 –7.86 Yes 0.00 1.09 No 0.00 –0.97 No 29.22 –11.30 No 5.33 –13.82 No 2.75 1.34 Yes 0.00 –16.51 No –1.45 2.40 Yes 4.86 –2.25 Yes –13.91 0.00 No 33.02 20.35 No –0.28 –14.42 Yes 10.67 28.49 No 5.49 –22.73 Yes 7.53 2.30 Yes 1.49 0.00 No 23.65 –38.12 Yes 30.21 –12.03 Yes 0.00 –8.41 No 0.24 –16.80 No 0.75 –4.45 No 40.75 0.00 No 10.04 1.13 No 6.17 –26.18 No 20.96 46.07 Yes 12.57 –18.42 No –10.16 –40.30 Yes 0.79 13.90 No 20.37 –3.19 No –8.20 0.00 No 10.28 0.00 No 16.02 0.00 No 14.11 5.34 No 5.74 –2.97 No 12.58 –11.21 Yes 19.37 4.28 No 15.23 –17.44 No 6.01 –38.22 Yes –12.24 0.00 No 8.39 0.00 No 25.42 24.29 Yes –11.05 117.20 No 0.00 –30.23 No 0.00 6.66 No –1.86 –21.50 Yes –2.90 –14.44 No 1.76 4.43 Yes 15.87 –11.60 Yes –8.48 –18.16 Yes 0.87 –0.65 Yes 0.00 –2.06 No 0.00 –15.75 No 8.64 –16.46 Yes –13.22 9.21 No 21.72 –10.25 No –4.73 –23.06 No 38.05 32.25 Yes 30.87 1.83 Yes 12.44 –44.97 Yes –18.91 0.08 Yes 44.25 5.00 No 0.00 7.22 No –4.93 –61.93 No 31.11 34.04 Yes 2.46 –12.94 No 0.00 8.76 No –22.71 0.00 No 23.41 25.22 No 0.00 –24.24 No –4.12 –84.29 No 8.77 –14.11 No 28.71 –20.00 No 0.00 –38.12 Yes 0.00 –11.81 Yes 13.77 –1.37 No –1.75 0.49 No –10.42 34.55 No –0.94 –20.70 No 16.90 28.27 Yes 0.00 –26.84 Yes 29.86 10.90 No 21.40 20.22 Yes 17.95 0.00 No 9.07 –0.97 No 34.56 36.31 Yes 32.64 0.00 No 0.00 –4.07 Yes 6.87 0.00 No 13.29 –19.98 No 12.73 –14.72 Yes –26.03 0.00 No 3.83 –17.86 No 9.10 4.06 No 8.54 14.51 Yes –13.58 –23.59 No 0.00 –18.52 No 23.84 4.80 No 0.00 –5.31 No 10.36 –27.65 Yes –17.64 –26.91 Yes 7.72 0.36 No 8.88 24.15 Yes 7.37 –35.22 Yes –0.76 2.50 No –2.24 –6.99 Yes 2.05 –18.14 Yes –11.39 –13.51 No 0.00 0.00 No 33.16 1.50 No 13.84 –27.03 No –1.20 4.64 No –12.61 –36.13 No –3.14 2.39 No 4.69 21.45 No 2.79 –1.10 No 24.90 0.00 No 6.61 –9.04 Yes 3.68 10.98 Yes –5.72 –11.19 Yes –4.49 5.86 Yes 0.00 0.00 No 24.48 –40.84 Yes 0.00 –18.35 No 14.61 0.00 No –5.21 –21.48 Yes 0.00 4.23 No 35.86 22.63 Yes 10.77 –8.17 No 0.00 –40.58 No 19.79 –40.09 No 29.44 17.56 Yes 29.92 18.61 No 18.74 24.24 No 16.73 –3.65 No 30.88 14.20 Yes 0.00 4.76 No –2.27 –15.60 No –5.20 11.34 No 63.09 12.56 Yes 26.58 –6.98 Yes 23.69 30.18 No 23.07 11.43 No –1.55 –8.27 No –3.63 –23.23 No 0.00 1.35 No 0.00 –52.84 No –16.06 0.00 No 9.31 –54.59 Yes 0.00 –2.98 Yes 16.12 –34.00 Yes 47.69 –1.39 No 4.26 –9.67 No 0.00 –26.76 No 24.25 25.85 No 7.44 –25.52 Yes 0.00 –17.23 No 10.89 –18.80 Yes 20.87 1.89 No –3.03 –22.30 Yes 4.10 –16.35 Yes
 SOURCE: http://www.ipohome.com; http://www.nasdaq.com.

 a-1. Estimate y = βo + β1x + β2d + ε where the dummy variable d equals 1 for firms that are high-tech. (Round your answers to 2 decimal places.)

 = + Price Revision + High-Tech

 a-2. Use the estimated model to predict the initial return of a high-tech firm with a 10% price revision. (Round your answer to 2 decimal places.)

 Initial return of a high-tech firm

 a-3. Find the corresponding predicted return of a firm that is not high-tech. (Round your answer to 2 decimal places.)

 Predicted return of a non high-tech firm

 b-1. Estimate y =βo + β1x + β2d + ε where the dummy variable d equals 1 for firms that are not high-tech. (Round your answers to 2 decimal place.)

 = + Price Revision − High-Tech

 b-2. Use the estimated model to predict the initial return of a high-tech firm with a 10% price revision. (Round your answer to 2 decimal places.)

 Initial return of a high-tech firm

 b-3. Find the corresponding predicted return of a firm that is not high-tech. (Round your answer to 2 decimal places.)

 Predicted return of a non high-tech firm

c.

In the above two models, determine if the dummy variable is significant at the 5% level.

 The dummy variable is significant since the p-value is less than 0.05. The dummy variable is not significant since the p-value is more than 0.05. The dummy variable is significant since the p-value is more than 0.05. The dummy variable is not significant since the p-value is less than 0.05.