Question

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

1) 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%

2) 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

3) 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

4) 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

5) 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

6) 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%

7) 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.

8) 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

9) 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

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

Answer 1

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)

Output:

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)

Output:

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