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Building type Average floor area (m2) Total floor area (m2) avg story height(cms) COST (HK$) 1...

Building type Average floor area (m2) Total floor area (m2) avg story height(cms) COST (HK$)
1 1852 81478 410 1467000000
1 1608 64313 411 1150000000
1 1430 55783 403 1028000000
1 1562 57794 390 1100000000
1 1109 37695 391 728000000
1 905 28048 382 558000000
1 1852 81478 410 1467000000
1 901 30617 391 631000000
1 1727 69062 400 1223000000
1 1161 37148 394 761000000
1 1004 37141 400 713000000
1 1216 38912 390 784000000
1 2007 88302 422 1593000000
1 2983 173000 440 2649000000
2 1523 70080 372 1210000000
2 912 28286 370 607000000
2 1343 53715 382 977000000
2 1175 32908 381 700000000
2 1203 40902 393 811000000
2 1393 52951 392 1001000000
2 713 20681 375 468000000
2 1047 37681 411 747000000
2 1506 63270 421 1156000000
2 1642 70624 423 1268000000
2 1848 73936 403 1333000000
2 1627 60190 402 1162000000
2 1301 40321 384 864000000
2 905 25330 405 561000000
2 1727 72514 400 1303000000
2 1414 52318 392 1013000000
2 2001 76022 431 1487000000
2 400 9200 380 263000000
2 3100 102190 454 2112000000
2 1677 83860 410 1519000000
2 2415 130032 420 2045000000
2 1555 46637 410 1025000000
2 792 20596 420 540000000
Building Type
1 Reinforced Concrete
2 Steel
2 Steel

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Run a regression model to estimate the cost of a building using average story height (mean centered) and total floor area (mean centered) as predictors.
Using the adjusted R Square statistic, how much variation in the dependent variable can be explained by the model?
Select one:
a. between 95% and 98%
b. above 98 percent
c. between 90% and 95%
d. less than 90%
Question 2
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Run a regression model to estimate the cost of a building using average story height (mean centered) and total floor area (mean centered) as predictors.
Is story height a significant predictor at .05 level?
Select one:
a. Yes
b. No
Question 3
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Run a regression model to estimate the cost of a building using average story height (mean centered) and total floor area (mean centered) as predictors.
Is total area a significant predictor at .05 level?
Select one:
a. Yes
b. No
Question 4
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Run a regression model to estimate the cost of a building using average story height (mean centered) and total floor area (mean centered) as predictors.
Which of the following is wrong about the slope of total area?
Select one:
a. It gives the expected change in the predicted cost for each 1 m2 change in total area, holding story height constant.
b. It is a significant slope
c. The expected cost of a building with a total area of 1 m2 is HK$13,965
Question 5
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Run a regression model to estimate the cost of a building using average story height (mean centered) and total floor area (mean centered) as predictors.
Which of the following is wrong about the slope of story height?
Select one:
a. It gives the expected change in the predicted cost for each 1 cm change in story height, holding total area constant.
b. It is a significant slope
c. The expected cost of a building with a story height of 0 cms is HK$3,185,038


Question 6
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Run a regression model to estimate the cost of a building using average story height (mean centered), total floor area (mean centered), and construction type (dummy coded) as predictors.
Using the adjusted R Square statistic, how much variation in the dependent variable can be explained by the model?
Select one:
a. between 95% and 98%
b. above 98 percent
c. between 90% and 95%
d. less than 90%
Question 7
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Run a regression model to estimate the cost of a building using average story height (mean centered), total floor area (mean centered), and construction type (dummy coded) as predictors.
Which of the following is correct about the intercept?
Select one:
a. It is the expected cost of a steel building with an average story height and an average total area.
b. It is the expected cost of a reinforced concrete building with an average story height and an average total area.
c. It is the expected cost of a steel building with a story height of 0 cm and an average total area.
d. It is the expected cost of a reinforced concrete building with an average story height and a total area of 0 m2.
Question 8
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Run a regression model to estimate the cost of a building using average story height (mean centered), total floor area (mean centered), and construction type (dummy coded) as predictors.
According to the model, is it significantly more expensive (at .05 level) to build a steel building compared to a reinforced concrete building, holding everything else constant?
Select one:
a. no
b. yes
Question 9
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Run a regression model to estimate the cost of a building using average story height (mean centered), total floor area (mean centered), and construction type (dummy coded) as predictors.
Which of the following is wrong about the slope of story height?
Select one:
a. it is the expected change in the predicted building cost for a one unit change in story height, holding total area and construction type constant.
b. Has a positive relationship with the cost of building
c. Has a negative relationship with the cost of building
Question 10
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Question text
Run a regression model to estimate the cost of a building using average story height (mean centered), total floor area (mean centered), and construction type (dummy coded) as predictors.
Which of the following is wrong about the slope of total area?
Select one:
a. it is the expected change in the predicted building cost for a one unit change in total area, in holding story height and construction type constant.
b. Has a positive relationship with the cost of building
c. Has a negative relationship with the cost of building

Solutions

Expert Solution

Import the data into R and store into a data frame dat

1)Option A (Adjusted R-squared: 0.9786)

R Code:

reg<-lm(dat$`COST (HK$)`~dat$`avg story height(cms)`+dat$`Total floor area (m2)`)

summary(reg)

Coefficients:

Estimate Std. Error t value Pr(>|t|)   

(Intercept) -1.007e+09 3.234e+08 -3.115 0.003724 **

dat$`avg story height(cms)` 3.185e+06 8.511e+05 3.742 0.000674 ***

dat$`Total floor area (m2)` 1.397e+04 5.043e+02 27.694 < 2e-16 ***

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 72020000 on 34 degrees of freedom

Multiple R-squared: 0.9798, Adjusted R-squared: 0.9786

F-statistic: 824.8 on 2 and 34 DF, p-value: < 2.2e-16

2)Yes,avg story height is a significant predictor at level 0.05 since pvalue=0.003724 < 0.05

3)Yes,Total floor area is a significant predictor at level 0.05 since pvalue< 2e-16 < 0.05.

4)c)The expected cost of a building with a total area of 1 m2 is HK$13,965

5)c). The expected cost of a building with a story height of 0 cms is HK$3,185,038

6)Option A (Adjusted R-squared: 0.9792)

R Code:

reg<-lm(dat$`COST (HK$)`~dat$`avg story height(cms)`+dat$`Total floor area (m2)`+dat$`Building type`)

summary(reg)

Coefficients:

Estimate Std. Error t value Pr(>|t|)   

(Intercept) -1.034e+09 3.197e+08 -3.234 0.00277 **

dat$`avg story height(cms)` 3.101e+06 8.420e+05 3.683 0.00082 ***

dat$`Total floor area (m2)` 1.406e+04 5.025e+02 27.987 < 2e-16 ***

dat$`Building type` 3.375e+07 2.434e+07 1.387 0.17480

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 71060000 on 33 degrees of freedom

Multiple R-squared: 0.9809, Adjusted R-squared: 0.9792

F-statistic: 565.5 on 3 and 33 DF, p-value: < 2.2e-16

7)d.) It is the expected cost of a reinforced concrete building with an average story height and a total area of 0 m2.

8)No it is not significantly more expensive since p value=0.17480>0.05.

9)c.) Has a negative relationship with the cost of building

10)c.) Has a negative relationship with the cost of building


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