Problem Set for Chapter 3: Simple Regression Analysis ECO382 Econometrics Queens College K.Matsuda

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1 Problem Set for Chpter 3 Simple Regression Anlysis ECO382 Econometrics Queens College K.Mtsud Excel Assignments You re required to hnd in these Excel Assignments by the due Mtsud specifies. Legibility is very importnt. []Use the following dt. Produce the Excel output of regression nlysis. Compre this lest-squres line in Excel output with your hnd-clculted lest-squres line. And comment. Tble 3.2 Exmple Dt x y [2]For ech of the dt sets discussed in this section, use computer to red the dt, construct sctterplot of y versus x, nd produce the regression output relting y to x. Exmple 3.2 Estimting Residentil Rel Estte Vlues The Trrnt County Apprisl District must pprise properties for ll of the county. The pprisl district uses dt such s squre footge of the individul houses s well s loction, deprecition, nd physicl condition of n entire neighborhood to derive individul pprisl vlues on ech house. This voids lbor-intensive reinspection ech yer. Regression cn used to estblish the weight ssigned to vrious fctors used in ssessing vlues. For exmple, Tble 3.5 shows the vlue nd size in squre feet for smple of Trrnt county homes (these dt re from 99). A sctterplot of vlue (y) versus size (x) is shown in Figure 3.5. Using sttisticl pckge, the regression eqution relting vlue to size cn be determined s VALUE -5, SIZE If size were the only fctor thought to be of importnce in determining vlue, this eqution could be used by the pprisl district. But obviously, other fctors need to be considered. Developing n eqution tht includes more thn one importnt fctor (explntory vrible) is discussed in Chpter 4.

2 Exmple 3.3 Pricing Communiction Nodes In recent yers, the growth of dt communictions networks hs been mzing. The convenience nd cpbilities fforded by such networks re ppeling to business with loctions scttered throughout the United Sttes nd the world. Using networks llows centrliztion of min computer with ccess through personl computers t remote loctions. The cost of dding new communictions node t loction not currently included in the network ws of concern for mjor Fort Worth mnufcturing compny. To try to predict the price of new communictions nodes, dt were obtined on smple of existing nodes. The instlltion cost nd the number of ports vilble for ccess in ech existing node were redily vilble informtion. These dt re shown in Tble 3.6 nd sctterplot of cost (y) versus number of ports (x) is shown in Figure 3.6. Agin, using sttisticl pckge, the eqution relting the price of the new communictions node to the number of ccess ports to be included t the node is COST 6, NUMPORTS Where NUMPORTS represents the number of ports. This eqution could be used to help predict the cost of instlling new communictions nodes bsed on the number of ccess ports to be included. Exmple 3.4 Forecsting ousing Strts Forecsts of vrious economic mesures re importnt to the U.S. government nd to vrious industries throughout the United Sttes. The construction industry is concerned with the number of housing strts in given yer. Accurte forecsts cn help with plns for expnsion or cutbcks within the industry. Tble 3.7 shows dt on the number of housing strts for the yers 963 to 996. Also shown re dt on home mortgge rtes for new home purchses (U.S. verge) for the sme yers. These dt were obtined from Business Sttistics of the united Sttes, 997 Edition. A sctterplot of housing strts (y) versus mortgge rtes (x) is shown in Figure 3.7. Note tht the reltionship ppers to be considerbly weker thn in the other sctterplots presented in this section. Intuitively, we might expect the reltionship between housing strts nd mortgge rtes to be strong one. But from the dt, this does not pper to be the cse. Perhps there re other vribles tht might be more strongly relted to housing strts tht could be used to provide ccurte forecsts for future yers. From viewing the sctterplot, mortgge rtes lone do not pper to be prticulrly to be helpful. 2

3 [3]Estimting Residentil Rel Estte Vlues (Continued). Wht is the smple regression eqution relting SIZE to VALUE? VALUE nd SIZE?. 4. Interpret wht this smple regression eqution mens. [4]Pricing Communictions Nodes (Continued). Wht is the smple regression eqution relting NUMPORTS to COST? COST nd NUMPORTS?. 4. A clim is mde tht ech new ccess port dds t lest $ to the instlltion of communictions node. Test this clim. 5. Interpret wht this smple regression eqution mens. [5] Forecsting ousing Strts (Continued). Wht is the smple regression eqution relting RATES to STARTS? STARTS nd RATES?. 4. Interpret wht this smple regression eqution mens. [6]Estimting Residentil Rel Estte Vlues (Continued). Wht percentge of the vrition in VALUE is explined by the regression? β β 3

4 [7]Pricing Communictions Nodes (Continued). Wht percentge of the vrition in COST is explined by the regression? β β [8] Forecsting ousing Strts (Continued). Wht percentge of the vrition in STARTS is explined by the regression? β β [9]Estimting Residentil Rel Estte Vlues (Continued) For n individul house with 3, squre feet, find prediction of its rel estte vlue. []Pricing Communictions Nodes (Continued) For n individul communiction node with 4 ccess ports, find prediction of cost. [] Forecsting ousing Strts (Continued) When the home mortgge rte is 6.5%, find the prediction of the number of housing strts. 4

5 [2]ABX Compny Sles The ABX Compny sells winter sports merchndise including skis, ice sktes, sleds, nd so on. Qurterly sles (in thousnds of dollrs) for the ABX Compny re shown in Tble 3.. The time period represented strts in the first qurter of 99 nd ends in the fourth qurter of Use Excel nd produce time-series plot of the sles figures. b. Wht does this time-series plot suggest? c. Use Excel nd get the regression output of the liner trend model y i β + βt + e i. d. Test whether the liner trend component is useful in explining the vrition in sles. Write down the hypotheses to be tested, decision rule using 5% level of significnce, nd decision. e. Use the liner trend eqution estimted by Excel nd forecst the sles for 2., 2.2, 2.3, nd