Question

In a study to examine the relationship between the time required to complete a construction project and several pertinent independent variables, an analyst compiled a list of four variables that might be useful in predicting the time to completion. These four variables were size of the contract, x1 (in $1000 unit) number of workdays adversely affected by the weather x2, number of subcontractors involved in the project x4, and a variable x3 that measured the presence (x3 =1) or absence (x3 =0) of a workers' strike during the construction. Fifteen construction projects were randomly chosen, and each of the four variables as well as the time to completion were measured. Answer the following questions. 16. What is the mean square error for the data? a. 240.3 b. 140.30 C. 157.86 d. 82.5 17. What is the linear equation for the case where there is no strike? a. Y= 1.59 - .01*size + .81*weather + 2.3*strike - 3.01*subcontract b. Y= 1.59 - 05*size + 28*strike + 2.49*subcontract c. Y=-1.25 - 01*size +.86*weather +3.72*subcontract d. Y= -1.59-01*size + .68*weather + 3.49*subcontract

time	size	weather	strike	subs
35	60	7	0	7
21	80	10	0	8
62	100	8	1	10
12	50	14	0	5
72	200	12	1	11
16	50	4	0	3
83	500	15	1	12
36	75	5	0	6
46	750	10	0	10
97	1200	20	1	12
7	70	5	0	3
23	80	3	0	6
30	300	8	0	8
56	2600	14	1	13
35	110	7	0	4

Answer 1

17)

Answer:

c. 157.86

Explanation:

The linear regression model is defined as,

ў = Во + B111 + Зух2 + 3х3 + 84х4

The regression analysis is done in excel by following these steps,

Step 1: Write the data values in excel. The screenshot is shown below,

A B с D E 1 у x1 x2 X3 X4 2 35 7 0 7 + 3 21 60 80 100 10 0 8 4 62 8 1 10 5 12 50 14 0 5

Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,

IE INSERT PAGE LAYOUT FORMULAS DATA REVIEW 000 - Data Analysis Х ? OK Cancel AZA Data Analysis Analysis Tools Fourier Analysis Histogram Moving Average Random Number Generation Rank and Percentile Regression Sampling t-Test: Paired Two Sample for Means t-Test: Two-Sample Assuming Equal Variances t-Test: Two-Sample Assuming Unequal Variances Help 36.6

Step 3: Select Input Y Range: 'Y' column, Input X Range: 'x1, x2, x3 and x4' column then OK. The screenshot is shown below,

A B с D E F G 1 Y X1 x3 x4 x2 60 35 7 0 7 2 3 ? x 4 5 6 Regression Input Input Y Range: Input X Range: OK $A$1:$A$16 mi1 Cancel 7 SBS 1:SE$16 RE mil 8 Help 9 Labels Confidence Level: Constant is Zero 95 % 10 11 12 SGS1 13 14 Output options Output Range: New Worksheet Ply: O New Workbook Residuals Residuals Standardized Residuals 15 LO Residual Plots Line Fit Plots 17 18 19 Normal Probability Normal Probability Plots

The result is obtained. The screenshot is shown below,

G H - K L M 1 SUMMARY OUTPUT 2 3 Regression Statistics 4 Multiple R 0.918524 5 R Square 0.843687 6 Adjusted R Square 0.781162 7 Standard Error 12.56421 8 Observations 15 9 10 ANOVA df 11 12 Regression 13 Residual 14 Total SS MS F gnificance F 4 8520.34 2130.085 13.49356 0.000487 10 1578.593 157.8593 14 10098.93 15 16 17 Intercept 18 x1 Coefficientandard Err t Stat P-value Lower 95%Upper 95% -1.25412 12.36332 -0.10144 0.921207 -28.8013 26.29306 -0.00771 0.006608 -1.16668 0.270406 -0.02243 0.007015 0.860731 1.060487 0.811638 0.435893 -1.50218 3.223643 27.31011 12.0619 2.264163 0.047035 0.434523 54.1857 3.720607 2.052662 1.812577 0.099981 -0.85301 8.294223 19 X2 20 X3 21 X4

From the regression output summary (ANOVA table)

Mean Square Error (or Mean Square of Residual) = 157.8593

18)

Answer:

c.

$Y=-1.25-0.01\times \text{size}+0.86\times \text{weather}+3.72\times \text{subcontract}$

Explanation:

The linear regression model is defined as,

ў = Во + B111 + Зух2 + 3х3 + 84х4

From the regression output summary (Coefficient estimate table)

$\widehat{Y}=-1.25-0.01x_1+0.86x_2+\27.31x_3+3.72x_4$

For no strike, x3 = 0

hence the regression model is now,

$\widehat{Y}=-1.25-0.01x_1+0.86x_2+3.72x_4$

19)

Answer:

b. surfaces are not parallel indicating an interaction effect.

Explanation:

We can see the interaction effect by plotting the line plot for the mean values. THe plot is obtained in excel by following these steps,

Step 1: Sort the data values.

Select all the data values then DATA > Sort > Sort by: x3, Sort On: Values, Order: Smallest to Largest. THe screenshot is shown below,

А B с D E F G H — x1 (2 x3 X4 1 Y 2 35 7 0 7 60 80 3 21 10 0 8 4 Sort ? 5 6 Add Level X Delete Level e Copy Level Options... My data has headers 7 Column Order Sort On Values 8 Sort by x3 Smallest to Largest 9 10 11 12 13 14 15 16 OK Cancel 17

Step 2: Calculate the mean value of all variables for the strike and no strike group. The mean values are shown below

...	Time	Size	Weather	Subs
No strike	26.1	162.5	7.3	6
strike	74	920	13.8	11.6

Step 3: Make a line plot. Select all the mean value then INSERT > Recommended chart > Line > Ok. The screenshot is shown below,

1000 900 800 700 600 500 400 300 200 100 0 Time Size Weather Subs No strike - strike

Conclusion: A parallel plot shows no interaction. From the above plot, we can observe that the lines are not parallel which shows an interaction effect.