3. Refer to the Real Estate data, which report information on the homes sold in

Question

3. Refer to the Real Estate data, which report information on the homes sold in the Goodyear, Arizona, area last year.

a. At the .02 significance level, is there a difference in the variability of the selling prices of the homes that have a pool versus those that do not have a pool?

b. At the .02 significance level, is there a difference in the variability of the selling prices of the homes with an attached garage versus those that do not have an attached  garage?

c. At the .05 significance level, is there a difference in the mean selling price of the homes among the five townships?

(Can you kindly use MiniTab if Possible)

X1 X2 X3 X4 X5 X6 X7 X8 263.1 4 2,300 0 17 5 1 2.0 182.4 4 2,100 1 19 4 0 2.0 242.1 3 2,300 1 12 3 0 2.0 213.6 2 2,200 1 16 2 0 2.5 139.9 2 2,100 1 28 1 0 1.5 245.4 2 2,100 0 12 1 1 2.0 327.2 6 2,500 1 15 3 1 2.0 271.8 2 2,100 1 9 2 1 2.5 221.1 3 2,300 0 18 1 0 1.5 266.6 4 2,400 1 13 4 1 2.0 292.4 4 2,100 1 14 3 1 2.0 209.0 2 1,700 1 8 4 1 1.5 270.8 6 2,500 1 7 4 1 2.0 246.1 4 2,100 1 18 3 1 2.0 194.4 2 2,300 1 11 3 0 2.0 281.3 3 2,100 1 16 2 1 2.0 172.7 4 2,200 0 16 3 0 2.0 207.5 5 2,300 0 21 4 0 2.5 198.9 3 2,200 0 10 4 1 2.0 209.3 6 1,900 0 15 4 1 2.0 252.3 4 2,600 1 8 4 1 2.0 192.9 4 1,900 0 14 2 1 2.5 209.3 5 2,100 1 20 5 0 1.5 345.3 8 2,600 1 9 4 1 2.0 326.3 6 2,100 1 11 5 1 3.0 173.1 2 2,200 0 21 5 1 1.5 187.0 2 1,900 1 26 5 0 2.0 257.2 2 2,100 1 9 4 1 2.0 233.0 3 2,200 1 14 3 1 1.5 180.4 2 2,000 1 11 5 0 2.0 234.0 2 1,700 1 19 3 1 2.0 207.1 2 2,000 1 11 5 1 2.0 247.7 5 2,400 1 16 2 1 2.0 166.2 3 2,000 0 16 2 1 2.0 177.1 2 1,900 1 10 5 1 2.0 182.7 4 2,000 0 14 4 0 2.5 216.0 4 2,300 1 19 2 0 2.0 312.1 6 2,600 1 7 5 1 2.5 199.8 3 2,100 1 19 3 1 2.0 273.2 5 2,200 1 16 2 1 3.0 206.0 3 2,100 0 9 3 0 1.5 232.2 3 1,900 0 16 1 1 1.5 198.3 4 2,100 0 19 1 1 1.5 205.1 3 2,000 0 20 4 0 2.0 175.6 4 2,300 0 24 4 1 2.0 307.8 3 2,400 0 21 2 1 3.0 269.2 5 2,200 1 8 5 1 3.0 224.8 3 2,200 1 17 1 1 2.5 171.6 3 2,000 0 16 4 0 2.0 216.8 3 2,200 1 15 1 1 2.0 192.6 6 2,200 0 14 1 0 2.0 236.4 5 2,200 1 20 3 1 2.0 172.4 3 2,200 1 23 3 0 2.0 251.4 3 1,900 1 12 2 1 2.0 246.0 6 2,300 1 7 3 1 3.0 147.4 6 1,700 0 12 1 0 2.0 176.0 4 2,200 1 15 1 1 2.0 228.4 3 2,300 1 17 5 1 1.5 166.5 3 1,600 0 19 3 0 2.5 189.4 4 2,200 1 24 1 1 2.0 312.1 7 2,400 1 13 3 1 3.0 289.8 6 2,000 1 21 3 1 3.0 269.9 5 2,200 0 11 4 1 2.5 154.3 2 2,000 1 13 2 0 2.0 222.1 2 2,100 1 9 5 1 2.0 209.7 5 2,200 0 13 2 1 2.0 190.9 3 2,200 0 18 3 1 2.0 254.3 4 2,500 0 15 3 1 2.0 207.5 3 2,100 0 10 2 0 2.0 209.7 4 2,200 0 19 2 1 2.0 294.0 2 2,100 1 13 2 1 2.5 176.3 2 2,000 0 17 3 0 2.0 294.3 7 2,400 1 8 4 1 2.0 224.0 3 1,900 0 6 1 1 2.0 125.0 2 1,900 1 18 4 0 1.5 236.8 4 2,600 0 17 5 1 2.0 164.1 4 2,300 1 19 4 0 2.0 217.8 3 2,500 1 12 3 0 2.0 192.2 2 2,400 1 16 2 0 2.5 125.9 2 2,400 1 28 1 0 1.5 220.9 2 2,300 0 12 1 1 2.0 294.5 6 2,700 1 15 3 1 2.0 244.6 2 2,300 1 9 2 1 2.5 199.0 3 2,500 0 18 1 0 1.5 240.0 4 2,600 1 13 4 1 2.0 264.2 4 2,300 1 14 3 1 2.0 188.1 2 1,900 1 8 4 1 1.5 243.7 6 2,700 1 7 4 1 2.0 221.5 4 2,300 1 18 3 1 2.0 175.0 2 2,500 1 11 3 0 2.0 253.2 3 2,300 1 16 2 1 2.0 155.4 4 2,400 0 16 3 0 2.0 186.7 5 2,500 0 21 4 0 2.5 179.0 3 2,400 0 10 4 1 2.0 188.3 6 2,100 0 15 4 1 2.0 227.1 4 2,900 1 8 4 1 2.0 173.6 4 2,100 0 14 2 1 2.5 188.3 5 2,300 1 20 5 0 1.5 310.8 8 2,900 1 9 4 1 2.0 293.7 6 2,400 1 11 5 1 3.0 179.0 3 2,400 1 8 4 1 2.0 188.3 6 2,100 0 14 2 1 2.5 227.1 4 2,900 1 20 5 0 1.5 173.6 4 2,100 1 9 4 1 2.0 188.3 5 2,300 1 11 5 1 3.0 A.1 Data Set 1-Goodyear, Arizona, Real Estate Sales Data Variables x, = Selling price in $000 x2 Number of bedrooms x3 Size of the home in square feet x, = Pool (1 = yes, 0 = no) x Distance from the center of the city in miles x6 = Township x, = Garage attached (1 = yes, 0 = no) Number of bathrooms 105 homes sold

Explanation / Answer

a) pool - x4

p-value of x4 = 0.008819434

since p-value is less than 0.02 ,   there is a difference in the variability of the selling prices of the homes that have a pool versus those that do not have a pool at the .02 significance level

b) attached garage - x7

p-value of x7 = 0.000011630

p-value < 0.02

hence there is a difference in the variability of the selling prices of the homes with an attached garage versus those that do not have an attached  garage at level of significance 0.02

c) township - x6

p-value of x6 =0.559330

p-value > 0.05

hence there is not a difference in the mean selling price of the homes among the five townships at  the .05 significance level,

Data

SUMMARY OUTPUT Regression Statistics Multiple R 0.730232318 R Square 0.533239239 Adjusted R Square 0.499555473 Standard Error 33.32950404 Observations 105 ANOVA df SS MS F Significance F Regression 7 123099.7575 17585.68 15.8307487 1.04429E-13 Residual 97 107753.0164 1110.856 Total 104 230852.7739 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 42.71590181 39.75663823 1.074434 0.285293449 -36.19001989 121.6218 -36.19 121.6218 X2 7.345403829 2.589575623 2.836528 0.005552458 2.205813048 12.48499 2.205813 12.48499 X3 0.038501524 0.014755286 2.609338 0.010508057 0.009216366 0.067787 0.009216 0.067787 X4 19.08623116 7.1402527 2.673047 0.008819434 4.914806068 33.25766 4.914806 33.25766 X5 -0.997225525 0.739655448 -1.34823 0.180724366 -2.465236843 0.470786 -2.46524 0.470786 X6 -1.562215947 2.666532661 -0.58586 0.559330019 -6.854545145 3.730113 -6.85455 3.730113 X7 35.52153676 7.682367716 4.623775 1.163E-05 20.27416343 50.76891 20.27416 50.76891 X8 23.12349991 9.062159715 2.551654 0.012283304 5.137621408 41.10938 5.137621 41.10938

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