Table 14.17The Least Squares Point Estimates for Exercise 14.51Bo = 10.3676 (.3710)B1 = .0500 (<.001)B2 = 6.3218 (.0152)B3 = -11.1032 (.0635)B4 = -.4319 (.0002)QuestionsUsing the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .05. Which independent variables are significantly related to y in the model with α = .05?Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .01. Which independent variables are significantly related to y in the model with α = .01?Find the p-value for testing Ho: βj = 0 versus Ha: βj ≠ 0 on the output. Using the p-value, determine whether we can reject Ho by setting α equal to .10, .05, .01, and .001. What do you conclude about the significance of the independent variables in the model?Calculate the 95 percent confidence interval for βj. Discuss one practical application of this interval.Calculate the 99 percent confidence interval for βj. 13.10Measurements Taken on 63 Single-Family Residences (for Exercise 13.57) OxHomeSalesPrice, yResidence (x $1,000) x,SquareFeet,SalesPrice, yResidence (x $1,000) x,Rooms, Bedrooms, Age.SquareFeet,Rooms, Bedrooms, Age.X2153.51,0082.2353363.01,05349.01,2906324363460.01,728350.58608252363534.0416449.991242413652.01,040552.01,2046403775.01,4963.655.01,204303.103893.01,936847.80.51,76483943960.01,9041,080643286.01,60073.194073.052469.01,2553.164171.01,768847410200.149.03,600104283.01,5031,736176141146.08643790.043161238.072083.0441441,6956.121349.51,0086.3.3545115.02,18681214105.01,9508524650.088823415152.52,086124755.21,1203.291685.02,0114764861.01,400331760.01,4656.310249147.02,1651858.51,2325 26950210.02,3538.1519101.01,7363675160.01,536352079.41,2966.1152100.01,9723721125.01,9963.9.5344.51,120272287.91,8742145455.01,6647.3792380.01,5805115553.4925202494.01,9203145665.01,2885.2574.01,4309 3165773.01,40021,4863275840.01,3761032669.06.1,0082.3559141.02,03812622763.067.51,2823206068.01,57229282935.01,1347461139.01,54562140.01,9931,13030142.52,4009.4156.213156355.02.92.21,701313.1656.01,02032 Supplementary ExercisesThe trend in home building in recent years has been to emphasize open spaces and great roome14.51community of Oxford, Ohio, had been building such homes, but his homes had been taking gemonths to sell and selling for substantially less than the asking price. In order to determine wubetypes of homes would attract residents of the community, the builder contacted a statisticianat a local college. The statistician went to a local real estate agency and obtained the data inTable 13.10 on page 518. This table presents the sales price y, square footage x, number ofrooms x, number of bedrooms x3, and age x4 for each of 63 single-family residences recentlysold in the community. When we perform a regression analysis of these data using the modely= B, + Bjx, + Bx2 + Bzx3 + BX4 + ɛwe find that the least squares point estimates of the model parameters and their associatedp-values (given in parentheses) are as shown in Table 14.17. Discuss why the estimates b. -6.3218 and baspecified square footage (1) to include both a (smaller) living room and family room rather than a(larger) great room and (2) to not increase the number of bedrooms (at the cost of another type ofroom) that would normally be included in a house of the specified square footage. Note: Basedon the statistical results, the builder realized that there are many families with children in a col-lege town and that the parents in such families would rather have one living area for the children(the family room) and a separate living area for themselves (the living room). The builder startedmodifying his open-space homes accordingly and greatly increased his profits.= -11.1032 suggest that it might be more profitable when building a house of aOS OxHome

Answered: Least Squares Point Estimates for…

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

Related questions

Question

Table 14.17

The Least Squares Point Estimates for Exercise 14.51

Bo = 10.3676 (.3710)

B1 = .0500 (<.001)

B2 = 6.3218 (.0152)

B3 = -11.1032 (.0635)

B4 = -.4319 (.0002)

Questions

Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .05. Which independent variables are significantly related to y in the model with α = .05?
Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .01. Which independent variables are significantly related to y in the model with α = .01?
Find the p-value for testing Ho: βj = 0 versus Ha: βj ≠ 0 on the output. Using the p-value, determine whether we can reject Ho by setting α equal to .10, .05, .01, and .001. What do you conclude about the significance of the independent variables in the model?
Calculate the 95 percent confidence interval for βj. Discuss one practical application of this interval.
Calculate the 99 percent confidence interval for βj.